TL;DR, a sizable chunk of it is fictional, though a lot of it (specifically relating to the notion of if he was a 'tyrant') is still under contention. He was not physically deformed, and I would argue his actions are somewhat unique, but not especially so.

You pose a pretty well-informed question, and I think a lot of emphasis needs to be placed on a specific word of it, specifically "uniquely". There are, of course, dozens of historical accounts arguing that he is that uniquely oppressive tyrant, where dozens still (typically more modern interpretations) range from a hazy "we may never know" to arguing a 'Good King Richard' viewpoint.

I do want to preface it all by stating quite clearly that there is certainly some "propaganda" and manipulation of information on both sides of the equation. For example, as your question revolves around, Shakespeare was a patron of the Tudors. "History is written by the victors" is a statement which very much applies to the Tudor dynasty, who had a vested interest in portraying Richard as a villain (in order to boost their own legitimacy as his usurper, something desperately needed given their relatively tenuous claim to the throne of England). But even that isn't unique - Richard III did not allow negative portrayals of himself to circle around, because he also was on pretty shaky ground as far as legitimacy goes. For example, William Collingbourne, a minor landowner and administrator, was executed for a one-line satire of Richard III and his aides:

"The Catte, the Ratte and Lovell our dogge rulyth all Englande under a hogge."

So while some suggest that the lack of negative commentary about Richard III's reign in his own time (AKA a time without "Tudor propaganda") indicates that he was not a tyrant or a bad king generally, the reality is that those who wanted to probably couldn't for fear of death.

That being said; probably the easiest point to discuss is that, no, he was not terribly deformed. He developed scoliosis in his adolescence, which we can see pretty clearly from his skeletal remains, and while it is generally "severe" by modern standards (to the extent that his right shoulder was higher than his left), researchers claim that it would have been relatively disguisable with clothing, and certainly it was not significant enough to impede him in battle, where he fought bravely in the thick of fighting, including at Tewkesbury and at Bosworth Field. Aside from that, there is nothing of particular note - though sources I've seen agree that he was certainly a somewhat sickly youth and not as physically attractive as his brothers (Edward IV, Edmund of Rutland, and George of Clarence).

Then comes the more complicated question, which is if he's an "oppressive tyrant". This is where our modern historical interpretations, while certainly advanced beyond repeating Tudor 'propaganda', are still quite divided. Certainly one of the greatest indictments against Richard III is the alleged murder of his young nephews, King Edward V and Duke Richard. If you subscribe to the argument that he is in fact the culprit - which is the majority opinion - is he unique in doing that? Somewhat, but not so much. Firstly, the killing of close kin was not particularly horrific; Richard's own brother, Edward IV, had his other brother, George of Clarence, executed on charge of treason. Second, the murder of deposed kings had not exactly been a unique trend in England - after all, they are potential threats to the successor's legitimacy. Hypothetically, any noble in opposition to the crown could lift up the cause of this imprisoned king; in other words, claimants are a tool that can be used against the monarchy. Accordingly, we see every single deposed king up to this point (Edward II, Richard II, Henry VI) dying in captivity, and almost certainly murdered (with the exception of Richard II, who supposedly starved to death, but even then there are arguments stating otherwise). What made the death of the princes unique was that all the prior examples of deposed kings actually had failures and justifications for their depositions in their own right; Edward V and young Richard of York were just kids. Of course, Richard III's justification for the deposition was that they were illegitimate, arguing that Edward IV already was married prior to his marriage to Elizabeth Woodville (mother of the princes), or even that Edward IV himself was borne from infidelity on the part of their mother. But at a minimum, it obviously does not look good for Richard. Distasteful? Absolutely. Unique? Somewhat, but not as much as some (especially the Tudors & their patrons) argued.

Other examples, such as his revocation of land from the elderly Countess of Oxford (seemingly with force) while he was still Duke of Gloucester, and his blatantly calculated executions of Earl Rivers (Elizabeth Woodville's brother) and Lord Hastings are often cited as examples of his tyranny and cruelty - again, in both cases, not unique. Particularly with the executions - pretty much every trial during the War of the Roses period was little more than a 'show trial' (when they were even given a trial prior to their executions).

I'm not going to go into the "Good King Richard" arguments, because they mostly deviate from the scope of the question (of if he was uniquely deformed or a tyrant), but know that he did bring about some changes (tax and law-related, specifically) that actually benefitted a lot of people, even at his own disadvantage, and that he is also somewhat unique in that regard.

So this was a very long (and yet very very condensed) run-down of some of the typically cited examples of Richard, and while you should bear in mind that it is all still pretty controversial and argued-over, I think most would agree that his actions are not particularly unique. Those that are 'unique' were developments across history which he took one step further (as his predecessors had done before him). Nobody had deposed a king up until Edward II. Nobody had deposed a king (Richard II) in favor of their own claim, and passed over the true line of succession until Henry IV did. Up until Richard III, nobody had deposed a king (Edward V) who themselves had not actually done anything wrong in a true sense. And so on.

EDIT: Looking back, I realized I glossed over his tendency to be somewhat 'light-fingered' with property rights, and didn't mention the threats and cajoling he did in his efforts to field an army to oppose Henry Tudor & the Lancastrian rebels. I somewhat touched on the former with respect to the Countess of Oxford issue, but it's worth specifying that he had issued attainders on rebels (depriving them of their lands/their family's right to inherit it) and, although most were pardoned (as is the norm), a sizable chunk of the seized lands were distributed to new lords from northern England (which served as Richard's primary base of power). This was, again, not really unique, though it did ruffle a lot of feathers among the southern gentry and populace, who now dealt with new lords that really didn't integrate with their lands at all; this impacted his image. The other point, relating to his issues with his lords and his efforts to force them into acting - the easiest (and most popular) example to give is Richard III holding the son of Lord Stanley (Henry Tudor's step-father) hostage, as a means of forcing Stanley to support Richard over Henry. He employed similar tactics where-ever possible to secure the support he needed to address the rebellion. While the scenario itself is rather dramatic (at Bosworth Field itself, Richard commanded that the son be executed when Stanley refused to move in his favor - Richard's retinue hesitated and instead suggested that they wait until the conclusion of the battle), I would actually regard this as pretty reasonable. The practice of taking hostages as a means of guaranteeing a lords' good behavior was very common, and while threatening one of your own commanders with a hostage on the battlefield was far from normal, it was more of a reflection of Richard's poor support amongst his lords rather than true 'tyranny'. He was essentially fighting tooth and nail to keep his lords in line and perform their obligations.

Bbb1227’s answer is great. Here’s another angle from u/Cheruthcutestory, though!