Lots of things all happening at once!
On top of the pain and everything else, it is common to feel this way about feeding at times. Often it eases off with a bit of time so if you can find a way to manage in the near term, maybe you'll buy yourself some breathing room to make it a slightly longer process. I'm not trying to talk you out of it, it's just that it is going to be very hard on both of you when he's sick and teething.
What do you do about the biting/positioning? Can you work on that to reduce your pain - take him off and put him down if he's hurting you maybe?
What help do you have? Can you partner take over during the night for a while (over the weekend at least, or for the first half of the night)? Do you get time out for yourself (probably desperately needed...?)