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.
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.