1) Obviously I cannot say when and from whom you acquired gonorrhea. You don't say what symptoms you had, but if there were no symptoms, you might have had it for several weeks, maybe even a few months. (Asymptomatic carriage of gonorrhea in the urethra is rare, but happens.) If you had typical symptoms (urethral dishcarge, pain on urination), the odds are you caught it 3-10 days earlier. Finally, perhaps you had a false positive lab test; the chance of that depends a bit on exactly what test was done.
2) The chance of HIV is low, although higher than it would be if you didn't catch gonorrhea. Your negative test result is highly reliable, but not perfect, since it was done only 3 weeks after your last sexual exposure. Have another test at least 6 weeks (many experts say 3 months) after that exposure to be absolutely sure.
3) I don't think it is possible to generalize about hepatitis B carriage by commercial sex workers. Blood tests for viral hepatitis are complex, typically including tests for hepatitis B virus itself, plus antibodies to types A, B, and C; and for HBV there actually are several different antibody tests that are commonly done. All these can become positive at different times. The provider who did the tests is in a better position than I am to tell you when your particular tests will be reliable in relation to the possibility of recent exposure. As you seem to realize, it is more likely that your abnormal liver function tests are chronic, not related to a new hepatitis infection. Whatever else happens, do follow up on that with your provider.
A final minor comment: the purpose of the doxycycline isn't to prevent syphilis, but to cover chlamydia. About 10-20% of men (and 20-30% of women) with gonorrhea also have chlamydia, and chlamydia treatment is routinely given to people with gonorrhea.
I hope this helps. Best wishes-- HHH, MD
I did have burning feeling in the tip of my penis but it went away. Prob irritation? Yea i know 3 docs is alot but two were at the same place at the same time. Not really flipping out about it i just dont want to move on with this and end up giving something to my girlfriend or having this comeback and bit me in the butt. The burning feeling comes back alittle bit after masturbation . Could this be just irratation as i dont use lube and im just noticing it cause im thinking about it? Thanks