So one of my arms is 0.5" smaller than the other

I've been always training with dumbells, but recently switched over to barbells hoping this would help me 'balance out' my biceps. My bicep on my left arm is smaller than my right arm. This is more than surely in part due to the rotator injury I had which has had me weaker in the left for a while. However I've been rehabing my rotator and even started training chest regularly, but now I have a smaller arm which is very lame when doing a double bicep shot lol.
A friend of mine told me that doing barbell curls will make the problem worse, to me it doesn't make sense as you are distributing the same load, but.. at the same time what he said kind of made sense, that the other arm will take the slack.. but does it?
With dumbells, I certainly had trouble on my left curls.
Need some advice on getting this sorted and no, I will not inject synthol.