R.S.
It sounds like you have a milk bleb and mastitis, coming from lots of milk flow with insufficient extraction of milk.
I have had a milk bleb before and it hurts a LOT. I can sympathsize...and the needle prick is what is usually recommended but the thiought of me stabbing my nipple while I am already in pain was crazy to me! I tried but could not go through with it. So what I did was soak my nipple in a bowl of water, as hot as I can comfortably tolerate, for about 10 minutes. Then, I used a manual pump to slowly tug at nipple and allow flow of milk down. It took about 45 min to break the bleb. I found this method worked very well and I recommend it to others. The warm water bowl technique opens up your flow ducts like steam opens pores in your face; but not using a cloth or anything to touch your skin directly allows you to expose your bleb to heat without actually touching it. I just filled a small bowl and bent over it, dipping my breast in the water. The manual pump allows for some control of the suction as you can tolerate, given that you are in pain. If you don't have a manual pump, hand expression should work fine as well...You Tube (of all places!) actually has some great videos on the techniques of hand expression.
I anticipate that once the bleb is fixed, the burning sensation you feel should dissipate. I am guessing this is a function of backed up milk flow causing inflammation driving up oxytocin (the let down hormone) -- thus causing the burning. This is the mastitis I am referring to.
No offense to OB's, but they carry such little education on -- honestly, you would have better luck asking random strangers on the street. Don't be surprised if your OB makes you feel like a weirdo because you are still breastfeeding. Better would be to contact your local La Leche League rep or to contact a lactation consultant.