You can test any time after 6 weeks with a third generation of HIV test for a conclusive. Or a IV Gen can be used for a shorter window period - 28 days.
Only an HIV antibody test is approved for primary diagnostics and can provide you with specific result.
No. Your pills can't interfere with your body's capability to produce antibodies to HIV infection, if you were actually infected.
If you were to be immunodeficient or immunocompromised you would have been spending a lot of time in and out of ER. Practically, no medicine except ARV drugs can interfere with an HIV antibody test.