Antibiotics
per se are unlikely to affect your ability to fly a plane, unless you have a massive allergic reaction (very unlikely) or feel the need to open the cockpit door and visit the latrines (very likely).
"Strong" painkillers are more likely to make you sluggish.
Codeine based products are most likely to affect performance, as the pain eases, NSAID's and paracetamol are very effective, (and likely to be more safe).
Chat with your AME
In the long term, the decision to remove the offending tooth will be one best taken with your dentist. From my experience, dentists tend to perform more quackery than doctors, check out NICE, I think they wrote something about this problem a few years ago.