You could have clogged ducts. You could probably call an OB or nurse help line for an opinion. Have you tried warm damp compresses? Place a warm wet washcloth on your breasts, this should releive some of the soreness and maybe even help unclog the ducts if that is the problem.
I am not sure what the white bump is. I get it on my right nipple. I relieve it every couple days as well. It has only a small amount of white in it (maybe the size of what comes out of a clogged pore on my nose) It is not sore, never has been. I wouldn't worry too much about it. I'm not worried about mine. Maybe I am wrong that it isn't a big deal, but I am not a doctor.
I hope it helps that someone else has it.