In theory, it's possible for you to have gotten an STI like syphilis or herpes, but syphilis would give you a painless, itchless sore, so it's probably not that. Herpes would give you blisters, so it's not likely to be that.
Also, you had really brief contact, which isn't likely to result in any transmissions of anything.
Nothing would be transmitted from him fingering you.
After this encounter, have you done anything differently than before? Did you use a lot of soap to clean? Use a wipe or anything? I don't think it's an allergic reaction to something you did that day only, but if since then, you've started using a different cleansing product or a wipe or anything, perhaps you have a reaction to that.
I'm not discounting your symptoms, but could it be anxiety? Do you notice less itch when you are busy and not thinking about it? Again, I'm not minimizing your symptoms. Anxiety can produce very real symptoms.
Try the cream the doctor prescribed. Lots of times, you need to use it after symptoms improve to make sure they don't come back. What was the first cream?