Milk on only one side??

My little guy is only 5 days old so we’re still learning and figuring things out. I’m using a nipple shield because he was 2 weeks early and had trouble latching. I’ve noticed that when he comes off my right breast there is definitely some leftover milk in the shield, but when he comes off my left breast there’s hardly anything leftover and what is there is still very clear... is it possible that my milk only came in on one side? He still seems satisfied from my left side and doesn’t complain, but is that normal? My left side has always been much smaller too, so maybe there just isn’t as much milk there? I try to offer the smaller breast more to increase my milk supply but I haven’t noticed a change.