OH! I SOOOO know how you feel. Not only did I have the same issues when my daugther started getting teeth, but early on in our nursing relationship we had several issues. One of which was latch issues and I had open sores on both nipples. Nursing WAS a labor of love for sure.
What I did was greased it up good with lanolin (Medela has a good one) and would nurse first on the unaffected side. This will help satisfy baby a bit and they won't be sucking quite as vigorously on the second breast. No, you don't really want to just nurse on one side. It will affect your supply. However, you COULD pump on the affected side. If you get the pump positioned really really well, it hurts much less. Just keep in mind that pumping is not like a baby sucking and it could also affect your supply.
For me, by nursing on the unaffected side first, helped a lot. The first couple of sucks on the affected side were that burning I want to scratch my eye balls out kind of pain. But it quickly subsided.
After you are done nursing, put some breastmilk on the open sore and let it air dry for a bit. Seriously, breastmilk is AWESOME as a healing agent. It has wonderful wonderful antibiotic properties. I even used it for pink eye! Somehow I ended up with pink eye, didn't think to use breastmilk at first, and went to the doctor. Got the normal regime, and it cleared it up. But, a day or so later I noticed my daughter was looking like SHE was coming down with it. So, I squirted some in her eye. Next day NO pink eye. A couple of weeks later I started having the same symptoms again. Squirt with the breastmilk. NO pink eye.
I know allowing the milk to dry on your nipple means your hanging out there for a bit and really won't work if you are out and about. If that is the case, put some lanolin on after nursing. It will help with the moist healing process.
It passes and suddenly it just won't hurt anymore. I'm sorry I don't remember how long it took.
Good luck!