I think you should see another doctor with a clearer understanding of STD's. The bumps you describe are very likely cysts rather than warts, but you need a definitive diagnosis. There are two viruses which could be relevant, as you obviously know: HPV or molluscum. Calling it "viral but not warts" suggests a certain fuzziness on the concept. For the reassurance you are likely to deserve, I advise you either to call your doctor and ask for clarification, or if that is unavailable or unconvincing, to see another doctor.
Best.
Dr. Rockoff