Why are you so paranoid about gonorrhea? All of this over frottage?
Frottage doesn't transmit gonorrhea, only penetration does. Even if you had gonorrhea, the first test, 24 hours after you took the antibiotics, would have a good chance of being accurate. I agree with your doc about it being about 80%.
A week later, I don't know - I wouldn't trust that result.
Kidney infections generally cause back pain, though that can differ a bit from person to person.
How long has it been since the encounter, and how long has it been since you took the meds?