Will bactrim cure Chlamydia and Gonorrhea?

Not at all. If you use these for this you will just piss away the drug and it will do nothing but delay your getting proper treatment.If you are assuming this is what you have, be aware that there are at least a dozed diseases that can pass through sexual contact.Some can be much worse than either chlamydia or gonorrhea.
Bactrim for STD. NO Please if you think you have either of these - see a doctor for the proper treatment. Taking antibiotics indiscriminately is dangerous.