No, only an HIV test will rule out HIV infection.
What was your sexual encounter?
If you tested positive for mono and the regimen they gave you worked, then obviously your symptoms were due to mono and not HIV.
There actually isn't any antibiotic regimen for mono that works. Mono usually goes on it's own in a few weeks, which is probably what happened. It does sound like your symptoms were due to mono and not acute HIV, but as Teak said, if you have had a risk for HIV, only an HIV test can rule it out.
Antibiotics don't work for Mono because Mono is not caused by bacteria, which is what antibiotics work against. Mono is caused by the Epstein Barr Virus. The treatment is rest, hydration, and possibly some over the counter medicines to treat the symptoms, like sore throat. There is no treatment for it. The diagnostic test is called a Mono-Spot test to test for antibodies made to something similar to the mono virus, called heterophile antibodies.
Just an aside, your symptoms correspond to mono because the incubation period (i.e. from the time you were exposed until you showed symptoms) is between 30 and 60 days (1-2 months). I think the ARS with HIV occurs sooner.