You can get a rash from anything, really.
It's not an STD - you wouldn't get symptoms nearly this quickly.
It could be fungal or friction, but the only way you'll know is to get it checked out. Stop trying to treat it yourself and let a doctor check it out. If it's fungal, you didn't get it from the drunken encounter - that wouldn't appear that quickly.
If you aren't sure you had sex or not, some STD testing would be a good idea.