Can store bought medication treat a sti?

No: Gonorrhea is treated with Ceftriaxone (it's injectable antibiotic), chlamydia with zithromax (oral antibiotic), trichomonas and bacterial vaginosis with Metronidazole (oral pill), hepres with Acyclovir or like drugs (pills), syphilis with penicillin shots. All of those are prescription meds, so the answer to your question is "no".

Not at all: If you are sexually active with infected partners, you must accept the need to have such diseases diagnosed and treated by health care providers. STD's can travel in pairs or groups & each often require a different treatment if there is any treatment available. Anything you get over the counter or from the net would delay proper treatment and add to the risk of long term complications.