I don't have a problem with my nipples. Thanks for asking though. :-
My buddy though, it doesn't matter what he wears they are going to bleed. I would suggest what others have and either wear a band-aide/nipple cover or use Glide.
I am not a doctor but from what I can tell if you have a part of your body that clothes rub on and it hurts, most times different clothes aren't going to fix the problem. Putting something between the clothes and the sensitive area will.
Personally, I think Glide is the best thing ever. I have a problem ehhhhhh between my legs and let's just say Glide makes Ms. SBS happy.
All this said, if you want my opinion on what shirts are the softest. I would say Mizzuno.