You can take them at the same time, though waiting a day might be a reasonable precaution for possible side effects.
Gonorrhea does not always cause horrible internal problems, but as was said, this is something you need to ask your doctor about and to see if you should take any tests to check for possible damages.
I'm in China at the moment and will be for the next year. I asked my Dr. but he didn't seem too concerned - maybe it was a communication problem, or maybe not. That's why I asked here......