They are tender because you just had your period. During this time, your chest will be extra tender and any sort of friction on your nipples or breast tissue may cause u some physical pain. They probably do not hurt while wearing the bra because the bra holds your breasts in place and they are not moving around.
I have the same issue as you. I have a D chest and I'm 23. My nipples are especially tender around period time. If you do not feel any lumps or are producing any strange discharge from your nipples, I think you are just fine, hun. I hope that helps.