31 weeks and fully vaccinated

I chose to get shot on my left arm and after a few hours... my left breast started to feel very swollen as if I need to pump kind of feeling. It started leaking before the 2nd dose though (1 week before) I've never experienced this with my previous pregnancies. Is it normal to have full milk before giving birth? I can literally pump now and give my toddlers lol. So much milk. It is so painful and swollen... should I start pumping but would it be enough for my newborn later on if I start pumping now? I still have about 6 weeks for at least 37 weeks (safe zone)