I am currently on meds for an abscess tooth. However the pain meds make me ill. Would something like bio freeze on my jaw line help with the pain?

Probably not. The pain is coming from within, not from the surface. Are you being treated by a dentist? Let them know about your condition.
Probably not. To tray an abscess requires specific dental treatment usually combined with antibiotic. Pain Meds block pain messages to brain, but do not affect a cure. Applying cold externally may reduce some swelling, but will not cure. Please see your Dentist. What you see as pain Med side effects may actually be response to the infection.
No. The pain is coming from inside your jaw. External treatment will not help.
Pain meds. Call the dentist treating you and ask for advice. He/she can suggest another pain medication and how best to tolerate any pain medication. That would be a better solution that using Biofreeze whichI believe would have no or little affect on pain from an abscessed tooth.