I'm on day three of taking clarithromycin for my severe strep throat and still haven't noticed any improvements. is this normal?

Many variables: It could be that you have a viral infection instead or at the same time and so the medicine is not helping the viral component, or it could be an issue of resistance or a very low dose of the medication

Yes and no: Sorry for the wishy-washy answer, but in reality if you have a "severe" case, it may take a while for you to feel a lot better. That being said, Clarithromycin is not my favorite drug for strep throat. Penicillin is still the gold standard, so unless you have anaphylaxis against the penicillin family, I would ask doc if they could switch you to penicillin or Amoxicillin.