Yes, they will cure both, and you can resume sexual activity after 7 days has passed.
And yes, condoms are always a good idea.
AJ
One more question. Will those medications cure any type of gonorrhea/chlamydia (oral/urethral)? Again I'm not sure if I have them, but just in case. Thanks.
Thank you for the reassurance. Does this also mean that I should be able to resume sexual activity? Obviously I will be more careful in the future. Thanks.
Yes, those will cure them (and good for you for knowing the names of the meds), but you should wait at least 3 weeks to test again, a month is better.
Sometimes dead DNA from the bacteria can linger, causing a false positive, or the meds can sometimes mask the bacteria - that's why you need to wait. You won't be infectious after 7 days though, assuming both treatments worked, which they almost always do.
Aj