Personally, i wouldn't do uni-latral movements, for stability/injury issues.
Just do dumbell oriented movements and see if that sorts it out. You may have a predominantly stronger side (which is natural since everyone tends to have a dominating side of their brain).
Stick at the lifting, be sure to "feel" the target muscle being worked and not just lifting the weight. In time you get the focus between mind and muscle and you'll be able to manage barbell movements and such without any associated "dominant" side.
Or you may be mistaking bodyfat distribution which you may hold strangely, a bit like myself (i'm leaner on my right side than left). This may give the appearance of a large pec, if you aren't totally clear how to distinguish between what is "fat" and what is muscle/water (not insulting your intelligence here).