Can you get a bacterial infection in your throat that's not from strep?

Yes -plenty of germs: Doctors can test for Group A Strep -which is only one specific germ that can cause a throat infection (or pharyngitis if you want to be technical). Different viruses are also implicated (like mono, adenovirus, etc) but certainly other bacteria are on the list. Pertussis (Whooping cough) and diphtheria are two important ones. Then there are other Strep species, 'mixed' infections like abscesses etc