Chlorine makes nipples burn?

So I am 34 weeks pregnant. Today we took our 1 year old daughter to a pool. Normally I have sensitive skin and worry about hers but this pool literally has a shower 3 feet away to rinse the chlorine off so I figured its ok and we rinsed right after and changed her into a dry diaper and clothes. So she is great loved the water had a blast. Meanwhile here I am already lactating a bit and leaking well my skin is fine but my nipples were like I had stuck them in a nest of fire ants... 😬 Like I mean they felt like I had rubbed them with flaming sand paper. I took another shower and it still wouldnt stop and my husband suggested squeezing my breasts. Literally I felt way better after finally giving into his suggestion and squeezing and self expressing a little bit. Has anyone else had this issue? I'm convinced chlorine got into the pore ducts and its made me not want to swim again in a pool because omg it hurt so badly and I dont want to have to milk myself to get it to stop again. 😭😭 I feel so badly like it was awful. Its also embarrassing hoping I am not alone and chlorine does this to someone else but if not warning it can happen.