The first thing is to confirm the diagnosis. Make sure that you have been tested (i.e. with a urethral swab or urine test) for gonorrhea or chlaymdia. This is important since there are different antibiotics to treat the different bacteria. If they don't work, then sensitivities can be considered to ensure that the bacteria isn't resistant. There are different antibiotic options to treat chlamydia (i.e. Azithromycin and Doxycycline).
Regarding liver damage, routine courses of antibiotics should not damage the liver. If this is a concern, routine liver tests can be considered for monitoring.
Some antibiotics are metabolized by the liver, and in cases of liver damage the antibiotics may not be excreted properly.
Followup with your personal physician is essential.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
Thanks,
Kevin, M.D.