It sounds to me like you are engorged. If you are pumping you could do that, cabbage is supposed to work as well.
Oh I remember this very well, your milk ducts are in overdrive at the moment! But over the next few days they will adjust to what your baby needs abd not make so much! Try a nice hot bath and speak to your dr if it doesn't ease as it could be a blocked duct
Try different holds - cradle, football, side-lying - baby will be able to get milk from different ducts that way. Keep nursing, use massage and warm showers as well. Make sure baby is getting a nice deep latch, with your whoooole nipple in baby's mouth, no pursed lips like on a pacifier. Does baby seem satisfied after a feeding? If not you definitely want to get in touch with a lactation consultant to make sure the latch is adequate to actually draw out milk. If you've nursed baby for 15-20 minutes on each side, baby is content and full, and you're still feeling uncomfortably engorged, you may want to pump off more milk (early on, it's common to have an over supply but your body will regulate over time). You can get milk storage bags at major retailers and freeze the milk for later on, after you've introduced a bottle (most IBCLCs say the best time for this is between 4-6 weeks to avoid disrupting the routine you're both trying to learn).
Mostly, just know that this sore and uncomfortable feeling is totally normal and almost always self-limiting. Your body isn't used to making all that liquid gold, or to storing it. The first month or so is the worst part and then it's easy as pie. Don't give up! You're doing a wonderful thing.
You can also try feeding your baby with baby on his/her back on the bed and you hovering over top. Also the supplement Lecithin is good for clogged ducts. But yes, feed often and it should start to feel better. Congrats and good job mom!
If your milk is just coming in it could just be the sensation from that which is uncomfortable. However you mention your breasts are hard in areas ... I assume you mean like lumps? If so it sounds like you might have a blocked duct. Even though it might hurt really bad the best thing you can do is keep feeding as the baby with help drain the blockages. Also have a hot shower and massage the hard areas ... again it might hurt but you really need to clear the blockages now or you will get mastitis. And you really don't want that! If its not getting better within a couple of days or gets worse see a doctor or midwife. Good luck and congrats on your baby :-)