Symptoms do not start that soon for any STD. I don't think this is a STD, but see a Dr for an exam. I see no reason for testing at this point.
STD's don't "come and go", unless it is Herpes or HPV, but I don't think either of these are your problem. It sounds like you're having an irritation or allergic reaction to the condom. As for the tip of the penis irritation, it may be herpes but most likely not...it is probably a minor urinary tract infection or non-specific urethritis (NSU)