I think it's really normal that you hear better on one ear.
I don't care due to the fact that my hearing is only like 70% of the average
hearing ability on my right ear and 60% on my left ear so
I did like 5 or 6 hearing tests since I am 1 1/2 years old, they give you coloured toys
which make some strange sounds and they ask you if you hear something
and put some electrods on your head stuff, my father said I thought it was game.
The tinnitus doesn't help very much but all in all I just get away with it.
If you start trying to hear certain things you will realize them, even if one ear hears a bit worse
(yeah this won't work if you're completely deaf), most people just don't listen carefully enough.
The left right thing only gets me when I record some guitars.
I use 2 impulses most of the time, pan 1 right and the other one left and I most of the time
the one on the left side is louder, but nowadays I just reverse the panning of the impulses for the
left track and the problem is solved