A month is probably unnecessarily long for that kind of pain. For both my first and second, it was about 7 or 8 days, and then it got much better, and then within a couple weeks after that absolutely no pain at all. I think, with proper training (you and the baby!) you can have even less pain than that! At the hospital, insist on seeing their lactation consultant twice if you can before you leave, and make sure to get the phone number of a lactation consultant who you can see after being discharged (most hospital lc's can't see patients privately). I know it seems like a lot of money (both of mine ran about $100 for a one hour appt and phone/email follow-ups), but it is WORTH IT. Make sure to get a good nursing bra that is easy to use, and stay hydrated and rested yourself. (Also, if this is number 2, consider "training" your oldest to sit quietly reading or watching a little video so you don't have to worry about him/her as you adjust to nursing again)
a little about me: SAHM of 2.5 yr old son and 8 month old daughter. I nursed ds for 15 months and am still nursing dd.