Can getting the flu shot while fighting a tooth infection with amoxicillin make you sick and cause vestibular weakness heart problems , dizziness etc?

POSSIBLLY: When you get a flu shot and have an underlying infection it could be affecting your immune system. I would recommend that you see your doctor.

No likely: Antibiotics do not interact with vaccines. It is safe to take them and get a flu shot. If you do have a reaction to a flu shot, the more likely reason for such symptoms would be an allergic reaction to a component of the vaccine. Contraindications to the flu shot include pre-exisiting allergies to gentamicin, neomycink polymnixin, thimersal, polysorbate 80, high fever, and others...