This is actually pretty well pointed out in the second episode when he deliberately puts himself on the right of Kate so that he can hear her using his left ear. He points it out explicitly that he needs to do this to hear her.

As for why he doesn't use a hearing aid on the other side, the most likely reason, although they haven't said it out loud, is that the other ear was too badly damaged to be able to use an aid.

Or he had some kind of issue with having one in that ear as well. Some people have trouble with that.

As a final thought, when the Avengers compound is destroyed by Thanos, and Hawkeye falls into the tunnels he fights the Outsiders in, he appears to be falling with trajectory to land on his right side. If he landed hard enough on that side of his head, there's no telling the severity of the damage he could have done to his right ear. But that's just speculation; there's no official answer to this yet.

https://youtu.be/49YEMeagIoI

Thanos Attack Avengers Base | Avengers: Endgame [Blu-Ray HD]YouTube