Hi there,
First of all, what was your exposure?
Also if a partner tested for positive for chlamydia its likley they did the "full" STI panel which includes
Chlamydia
Gonorrhoea
HIV
Syph
You didnt mention if the chlamydia was oral or not which changes the testing method but that being said, if your partner did the whole panel and only chlamydia came up then it is safe to say they did not have gonorrhoea which means you do not either.
If you tested 4 week after the antibiotics then that result should be accurate.