J.A.
First off, congratulations on the new arrival and successfully breastfeeding!!
I had the same problem for the first few months (I had an insanely abundant milk supply). At night I would have to wear an absorbent nursing bra with nursing pads in it. Sometimes I'd have to change the nursing pads in the middle of the night. That helped. Until he started sleeping through the night and I wasn't waking up to change the pads!
As for the sore nipple. I also had this problem. I talked to my lactation consultant about it and she thought it was do to improper positioning. After doing some slight adjusting I got more areola into his mouth and within a week the soreness was completely gone and never returned.
Good luck! I hope you find something that works for you. Breastfeeding is a little bit of trial and error :)