Depending on the location, can you get a waterproof dressing and put it on to take the strain whilst feeding?
If you give him the side that is working more often it will kick up its milk supply over a couple of days to match too.

You need to offer your LO lots of cuddles even if you're not feeding - he's probably at the point where feeding is as much about snuggly time when he knows Mum must be there as it is about the milk.