Booth was a relatively well known actor at the time, his was not just some Joe off the street. His performances had been seen by thousands, and his family had produced multiple well known actors including his brothers and father.

So when he shoots President Lincoln in a crowded theater, then jumps to the stage and shouts "Sic Semper Tyranus" people, doubly so for being the crowd at a play, knew who he was quickly. Thousands had photos of him in albums or posters from his acting career before the war as well. We should also note it is possible to likely he injured his leg during the jump, though he claimed to the doctor who later splinted it, that it had occurred when his horse fell on him and there isn't 100% proof either way.

That said he did manage to escape from DC itself, which while still heavily occupied by Union troops was in a state of heavy activity following the surrender of Lee and the collapse of the Confederacy. Booth does escape into very rural Southern Maryland, first to the inn of Mary Surratt where he had stashed supplies, for this and her other assistance to the cabal she would be hanged as an accomplice. Then later to Dr. Mudd's where his leg was treated, and on to a nearby farm to hide in the nearby woods. By this point two days or so had passed and already there was a $100,000 bounty for him and federal troops dispatched to search for him or clues, while Booth waited for a chance to cross into Virginia and what he hoped would be more safety.

Booth reaches Virginia on April 23, a week after the assassination, and is led to a farm owned by the Garrett family where he hides in a barn, like with the Mudd house his true name is not revealed to them and initially the Garrett's were unaware yet of the killing. However by tracking those who aid him through tips, investigations, and patrols Union cavalry and intelligence officers begin to close in. Finally in the early morning of the 26th, having interrogated the man found to have led Booth to the farm a detachment of Union cavalry arrived, and when Booth's companion David Herold surrendered, Booth retreated to the barn which was lit on fire and he was shot while inside by one of the troopers.

So by 1865 photography, telegraphy, the nature of Booth's status, and the nature of the killing made it very difficult for him to escape for long, in an area which had already been under Union military occupation for 4 years.