Yes you did have chlamydia. Why is it not going, well reinfection is the usual reason. Did your partner have a negative PCR DNA chlamydia urine test two weeks after taking her medication?
There is little chance of a false positive PCR test, it looks for the actual DNA of the chlamydia bacteria.
The important thing is to take your antibiotic, wait two weeks, get a proof of cure test and then you can move on.
No, you should be all good.