Moriah... (I am in your due date club, but will respond here). Sorry you are dealing with this now and that you are in pain. You will come to a plan that will work for you, but here is what I would do...
If possible (the infection isn't worsening and the dentist is ok with it), I would hold off on surgery until at least day 5 after birth (maybe longer if you are not in terrible pain). By then, your milk should be on its way to coming in and you will have established your breastfeeding relationship. Having drugs in your system isn't ideal, but if you have mamas willing to provide you with milk for a couple feedings, you could pump and dump for the 12 hrs after your surgery (or less...sedation drugs are actually very short acting and clear from your system quickly - maybe check with a lactation consultant to find out the half life of the specific drugs you will be taking, or look them up online). I would have someone else finger or syringe feed the baby during that time, then resume breastfeeding. Fortunately, wisdom teeth removal is usually a pretty quick, in and out procedure and you can be home within a few hours, snuggling with your baby. If you are not already, start taking probiotics and if you are on antibiotics after surgery, get some probiotics for your baby as well.
If you want to pump your own milk starting on day 3-4 to use for the few hours when you wouldn't be breastfeeding, you could do that also. I have personally been dealing with engorgement...so I would NOT pump during that time, because it would signal my body to keep overproducing. Also, every body is different, but I am now a week post-partum and my supply is evening out to a good amount where I wouldn't be concerned about having to leave the house for several hours without my baby if I absolutely had to (as for surgery).
One other thing (and I totally don't mean to downplay your situation, because it stinks!!!) is that despite our ideal plans for birth and beyond, things come up that interfere (silly, crazy, life!!!) and being a mom is about letting go of some things we wish we had control over. I had been sick the week before my birth, was just starting to get better when I birthed. It must have put a strain on my body, because the next day, I got sick again. My first week with my sweet, sweet girl has involved me having nightly fevers, a horrible cough that strained all my abd. muscles and uterine ligaments, sinus pain, laryngitis and now earaches. I hate that I keep coughing all over her and can't enjoy her sweet newborn smell. Oh, and my babe is tongue-tied (we still need to get it clipped), so I have been dealing with sore, bleeding nipples as well. Not exactly my perfect vision of my first week with her, but we will get through and you will too.
Good luck! I hope you come up with a plan that brings you peace.