Can I feed from just one breast?

My baby is 6 weeks old and breast feeding has been the most difficult thing being a mum. The last 2 days my right nipple is horribly sore, I've tried to use a nipple shield but he gets frustrated because I don't think enough milk is coming out. I know it's more painful on this side because he doesn't latch on properly. It's now got the point I can't even attempt to feed him on this side because the pain is so unbearable.