I'd go to a doctor if you can. They may be able to give you some pain medication for it. If you're engorged on that side, a stronger pain med once a day may help relieve the pain enough to empty the breast. Check with kellymom.com for lactation-safe meds. I know the kind of pain you're going through. I nursed my little guy for 6 months with a tongue-tie and screamed half the time he latched on. It would hurt so bad I could taste the bitter, metallic adrenaline in my mouth.
Try also taking the recommended dose of ibuprofen about 30-40 min before the next nursing session - it may help bring the pain to a manageable level & help relieve swelling. Don't fret too much about your supply, either, your other breast will accommodate your LO in a little while. My left one started producing more (& still does) b/c that's the side DS sleeps on.
It's possible the tissue is still swelling, squeezing some ducts closed. I'd keep that breast naked as much as possible and use cool & cold compresses (not ice, refrigerate some small baggies of water & wrap in a thin fabric & only use on the specific injured area, so the nipple) to help get the swelling down. Warm compresses may make it feel better, but will bring back the inflammation. If you are feeling pain up higher in the breast, it may be from "backed-up" milk.
Can you hand-express, or is that too painful as well? If you can, while you hand-express, try using a little bit of warmth on the area that is swollen (where all the milk is backed-up) to help relax those glands & let the milk flow. If you can get the positioning correct, try cool compress on the nipple, remove it, then latch your LO on the "good" side & use a warm compress higher up on injured breast with a little massage (gently rubbing from the outside of your breast toward the nipple) while your little one nurses on the uninjured breast. Hopefully that will trigger let down and help relieve some of the engorgement on that side. Between cold compresses and ibuprofen, you may be able to tolerate a minute or so of nursing to help relieve any engorgement. Just be sure to reapply the cold compress when you're done.
Hope you feel better soon!
Nipple damage really can hurt worse than childbirth.