I still believe his head was deformed by an accident in a game of dodge ball when he was little
exhibit A
the series bible states Edd had some sort of indecent in a game of doge ball years ago
"He hasn't been allowed to take gym ever since an indiscretion during a Dodge ball game. He’s excused to spend free study time in the library."
exhibit B

underneath edd's shower cap his head seems to be deformed and bumpy
exhibit C
Edd is scared shittless of doge ball in the episode ed in the half shell

he says "Eddy, wait! I-I have a history with this game. I-what's that? Deep flashes, Eddy, like tentacles! Strangulating every rational nerve! Oh, I'm reliving it, Eddy!"
Exhibit D

he had to move to a new town when he was a tot for unexplained reasons
Exhibit F

in the big picture show when edd loses his hat ,keeping in mind they've already seen what's under there before, eddy still react as though it's hard to look at and ed asks "does it hurt"

Actually, the game was not created by the same people who created the show and was later confirmed non-canon. HOWEVER, Danny Antonucci, the creator of Ed, Edd, n Eddy, said that he when he was designing Edd, he gave him a hat based off a time in his youth where he burned some hair off his head and wore a hat to hide it from his parents. Many speculate Edd may have a scar due because of this, but what's actually under his hat has never been confirmed by Antonucci.