You can use Mupirox ointment (containing mupirocin) at the same time for the infection around the ear piercing and take Augmentin (amoxicillin with clavulanic acid) for the tooth infection. Mupirox acts topically and is not absorbed significantly into the bloodstream, so it does not interact with systemically used antibiotics such as Augmentin. This combination of treatments is safe and often used for simultaneous local and systemic infections.

I have attached helpful materials:

https://www.gdziepolek.pl/artykuly/fakty-i-mity-o-antybiotykach

https://www.gdziepolek.pl/blog/antybiotyki-czy-przestana-dzialac