Hi - Minocycline may give you a false negative on an STD test for gonorrhea and chlamydia. (Any antibiotic would.)
Depending on the dose, it may cure gonorrhea, though there is some resistance to it now with certain strains of gonorrhea. It MAY prevent you from getting it, but the studies done that showed it would are quite old, and were done before resistance.
All that said, oral sex is lower risk, even for men who have sex with men. Even though with men it is a higher risk than for oral sex with women (the penis often gets into the throat where bacteria resides, which obviously isn't possible with the vagina), it is still a lower risk than genital to genital or genital to anal sex.
I'm not sure why you are taking the mino, but if you are concerned about this, it would warrant a talk with your doctor.
Best of luck!