I had a friend who was very self-conscious about her nipples. She used to wear band-aids over them whenever she was wearing a tee shirt or something that might let them show through or even just poke out a bit.

You can get them in various sizes, and as far as I know they stay on pretty much all day. If you have chest hair, maybe look for something a bit less aggressive when it comes to removing them.

Unless you’re into that.