Bacterial vaginosis causes a fishy smelling discharge and commonly reoccurs if you keep doing the things that upset your vagina's normal pH. E.g. baths, douching, vaginal 'cleaning' products, over washing, although sometimes no obvious cause. It is diagnosed by a swab and usually treated with the antibiotic metronidazole- penicillin wouldn't treat it.
Thrush can be resistant to initial treatment and can quickly recur so the fact she didn't respond doesn't mean it isn't thrush. Thrush discharge is commonly white, curdy, cottage cheese, itchy, sore.
STIs are more common in kids than we expect, and sometimes they do deny having had sex until there is irrefutable evidence, so if the Dr suggests an STI swab I would encourage her to have it (she can do it herself), at the least to rule this out.
A self swab is a good idea, as long as she manages to swab enough of the discharge to get a result.
If she isn't getting any joy would she consider an external examination e.g. just looking at the outside of her vagina? It sounds odd, but if you have a good GUM clinic near you (most likely if you live in a large city) they will be used to putting people at their ease and examining young people.