Unlikely that you get any STDs from brief penis rub. I would be more confident that it is a thrush than chlamydia. Either way, lets give your medication a few more days to work out. But generally, you should feel much better with medication. Otherwise, head back to the doctor.
Extremely low risk to zero for chlamydia for brief exposure. Dont bother.
That's not true btw, only HIV cannot survive outside the body.