I took two pills of azithromycin to treat chlamydia but I threw up an hour and fifteen mins later. Did I absorb the antibiotic or do I need to take it again?

Enough absorbed. This has been studied. You probably absorbed enough. The research showed that most of a one gram dose of azithromycin for chlamydia is absorbed and treatment effective if vomiting is more than 30 minutes after taking it.