Female vaginal swab test for ureaplasma was negative after treatment with azithromycin and moxifloxacin. but can it possibly still be in my urethra?

Very unlikely: the way the organism gets there is either from above - i.e. from the bladder and then down the urethra and out to the world - or ascending from your skin,from you or your partner and then back up the urethra into your bladder. You state that after treatment a culture was taken and was negative!. So if you got it again it would have to be a new infection from either you or your partner!