if you go to a department of health they usually only charge you based on what you can afford so if you can't afford anything they won't charge you...good luck
Gonorrhea can be transmitted through oral sex, although this is rare, and clamydia cannot. Neither can be transmitted from kissing or sharing a drink. Gonorrhea of the throat is typically asymptomatic and is usually cleared by the immune system without treatment. Do you know if your friend has gonorrhea of the throat?
If your only exposure is by sharing a drink, then I really doubt that your throat bothering you is from some sort of STD. It could be upper respiratory infection, or you are just anxious and worried about it.
Hope this helps.