Can taking clarithromycin make my teeth ache?

No: In fact it is a great antibiotic for bony tooth infections.

Not usually: Clarithromycin is an antibiotic used to treat a variety of infections. It does have a fair amount of adverse affects but toothache is not one that is listed. About 2% of the patients experienced headaches during trials of this medication. If you don't have any oral problems it may be an adverse effect but if you are not sure then a trip to the dentist is advised to rule out tooth related problems.

No, but cavities, gum disease, parafunctional habits, fractures, malocclusion, systemic diseases, etc. can. If your teeth hurt, see your Dentist.