I will attempt to answer this question to the best of my ability. However, I am a mere undergraduate, so I will purposefully limit the scope of my answer to a single group of Celtic people described by the Greek historian Polybius. Classicists (or Celticists), please feel free to correct my translation of the Greek or any other aspect of my answer.
As far as I can tell, the earliest Roman or Greek account of Celts fighting naked can be found in the Histories of Polybius. In describing a Roman battle against the Boii, Insubres, and Gaesatae (three different Celtic peoples), he writes:
οἱ μὲν οὖν Ἴνσομβρες καὶ Βοῖοι τὰς ἀναξυρίδας ἔχοντες καὶ τοὺς εὐπετεῖς τῶν σάγων περὶ αὑτοὺς ἐξέταξαν. οἱ δὲ Γαισάται διά τε τὴν φιλοδοξίαν καὶ τὸ θάρσος ταῦτ᾽ ἀπορρίψαντες γυμνοὶ μετ᾽ αὐτῶν τῶν ὅπλων πρῶτοι τῆς δυνάμεως κατέστησαν, ὑπολαβόντες οὕτως ἔσεσθαι πρακτικώτατοι διὰ τό τινας τῶν τόπων βατώδεις ὄντας ἐμπλέκεσθαι τοῖς ἐφάμμασι καὶ παραποδίζειν τὴν τῶν ὅπλων χρείαν (2.28).
Already the Boii and Insubres drew out in battle order wearing trousers and close-fitting cloaks around them. But the Gaesatae, due to pride and audacity threw away these things, arranged themselves in the front of the military force, naked with their weapons; assuming that this would be the most practical, since the ground was overgrown with thorns, which may tangle their upper garments and hinder the use of their weapons
Polybius may be exaggerating just a bit to emphasis the contrast between the Gaesatae and the Boii and Insubres; he later reports that the warriors of the front line were κατέχοντες σπείρας χρυσοῖς μανιάκαις καὶ περιχείροις ἦσαν κατακεκοσμημένοι. (richly adorned with gold neckless and bracelets, 2.29). Nevertheless, Polybius does seem to verify that a specific group of Celtic people fought practically nude. There are other accounts of different groups of Celts fighting nude in antiquity (see Livy 22.46), which help bolster Polybius’ claim. Furthermore, Polybius's emphasis on the importance of accurately recording historical events and source criticism set him apart from other historians (Derow). In short, he’s considered fairly reliable. (There’s a reason Mommsen called him the “sun in the field of Roman history.”) Though, it has been argued that good old Polybius may have got the reasoning for the Gaesatae’s nakedness wrong. Rankin asserts that the nakedness of the Gaesatae was ritualistic in nature, rather than born out of a utilitarian purpose (Rankin 74, 115).
I can’t seem to find any sort of account in the Natural History where Pliny reported that Celts fought naked. Your friend may have gotten his/her ancient sources confused. I also have absolutely no idea where the idea that they fought with erections came from.
If you would like a more in depth and well written account, try to get a hold of Celts and the Classical World which I cited twice. Mods, I hope this answer is up to the standards of the subreddit. If not, delete it.
Sources (modern):
Edit: fixed a few typos and formatting issues.
Where exactly does Pliny the Elder mention this in the Natural History?
I actually wrote a pretty long post about this on r/badhistory a long time ago! Most of the images that I reference can be seen in the original post
Part I: Introduction & Literary Representations of Gallic Nudity in Battle
Many of you are probably familiar with images such as these, which depict totally butt-naked and buff Gallic warriors recklessly running into combat or thinking about killing some dudes. Exposure from such depictions in paintings, video games and sculptures gives many people the impression that naked combat was a common occurrence in Gallic warfare, as evidenced this really bad wiki page and blog post. I would instead argue that depictions of Gallic nudity have their roots less in reality than in Classical depictions of the Gallic body (particularly Hellenistic ones), which were meant to emphasize the Gauls’ reputation as relentless and fearless noble savages. Classical depictions of naked Gauls share another related characteristic: the naked Gaul is always defeated or faces inevitable defeat by the creators of the representation. Naked Gauls are thus less of an accurate representation of reality than propaganda pieces that implicitly exalt Hellenistic or Italic polities/civilizations while honouring the perceived savage nobility of the Gallic warrior.
The reason I started writing this post was because I was actually doing research to write another badhistory post about a website which, among other things, claimed that the ‘Celts’ regularly went into battle naked. Strangely enough, I could find few credible secondary sources on Gallic nudity and decided to look further into the subject. So what primary sources do we have to consult? Unfortunately the Gauls used writing for mundane purposes, curse tablets and calendars but not much else, meaning that we have to rely on Roman and Greek sources, most of them second-hand.
Diodorus and Polybius are the two most-cited authors on the subject of Gallic nudity, but neither author presents a very convincing depiction of regular naked combat amongst the Gauls. Polybius’ recounting of the Battle of Telamon describes how the Gaesatae, who were probably an elite force of unlanded warrior-aristocrats, got naked before battle:
The Insubres and Boii wore their trousers and light cloaks, but the Gaesatae had discarded these garments owing to their proud confidence in themselves, and stood naked, with nothing but their arms, in front of the whole army, thinking that thus they would be more efficient, as some of the ground was overgrown with brambles which would catch in their clothes and impede the use of their weapons.
So the Gaesatae definitely got undressed before the fight, but Polybius is very clear that this had a practical purpose; the ground they were fighting on was covered in brambles and they didn't want to get caught up in them. So we have one concrete example of Gallic nudity in combat, but it has little to do with a regular practice of naked fighting but was instead inspired by battlefield conditions. It may be that the Gauls were more prone than folk like the Romans to undressing before a fight depending on the circumstances, but it was hardly a common occurrence. So what does Diodorus have to say about the subject?
In his Library of History, Diodorus Siculus provides a pretty decent description of Gallic arms and armour, stressing the quality of their shields, bronze helmets and chain mail cuirasses (a novelty invented by the Gauls in Europe and later adopted by the Romans) before stating: "Some have armour made of iron wrought in chain fashion, while others who fight naked ward off [attacks] by/with what was given to them by nature" (thanks for the translation /u/celebreth :D). This is a very general statement, written by a man who lived nearly two centuries since the Battle of Telamon, which alongside Classical depictions of the naked Gaul (which I will discuss shortly) probably influenced Diodorus’ statement.
Surely if the Gauls regularly fought naked, a firsthand account of a war with the Gauls would mention it. Interestingly enough, I could find only one mention of Gallic nudity in Caesar’s Commentaries on the Gallic Wars, which doesn’t even depict a Gaul in battle. In Book 7, Chapter 46, Caesar describes how the Aquitainian king Teutomarus, after being surprised by a Roman assault on his camp “with difficulty escaped from the hands of the plunderers, with the upper part of his person naked, and his horse wounded.” So the one naked Gaul in Caesar's entire account is only partially dressed because he literally had no time to put clothes on before fleeing. Hardly convincing evidence of regular Gallic martial nudity. Why is Caesar’s account’s lack of nudity significant? Because it suggests, I think, that Diodorus’ secondhand account is more reflective of an imaginative picture of Gallic customs than an accurate representation of reality. It is possible that the Gauls of Caesar’s time had simply stopped going into battle naked, but I find the former theory more convincing.