Nipple Skin Peeling

So I am currently 34+5 weeks pregnant and for a while now, at least a couple weeks, my breast have been itching and my nipple skin had been peeling like crazy. It’s to the point where if i take my bra/shirt off there will be skin all in it. I’ve been keeping them moisturized with olive oil, which is what I use on my stomach, and it kind of relieves the itching until it gets dry again. I’m just concerned on how this will affect me breastfeeding. I feel like if it continues, the baby will definitely be getting a little skin in his mouth after feeding😭 Does this go away eventually??