Sensitive nipples
I'm in my late teens and have always had sensitive nipples. Usually when I ovulate or during my period they get erect easily, and poke out an inch or so. Wearing bras was uncomfortable and tended to give me rashes, so I recently stopped wearing them. I feel so much better.
I live at home still and my mom has been trying to get me to wear bras again. She's even tried to take me shopping for something softer that might irritate less. I don't really care at this point, I don't like bras.
What my mom doesn't know is that I also like being topless this time of year after she leaves for work. It's hot in the house and we have no air conditioning. It's nice to let the tits out when I'm having coffee in the morning and playing on the computer. My dad works from home and he doesn't care. Tits are just tits and it's nice to let them free.
Sounds to me like you're wearing the wrong size. I'd get re-measured. For a about a year when I was young I was a little uncomfortable because I had put on a little weight and went from a 36 to a 38. My cup size didn't change, but the band size did. Once I got bras that finally fit, they felt fine.
Considering you are a guy, it should be no problem. But you may want to lose some weight if you're so big that you have man boobs and need a bra.