First, there is no STD that will give you symptoms within hours. The absolute minimum is 2 days. I don't know what caused your symptoms that night, but it wasn't an STD. I don't know if you've been vaccinated for Covid, but could that have caused your symptoms and the timing might have been coincidence? It sounds an awful lot like covid to me.
The IgM for herpes is a really unreliable test. It's wrong at least as often as it is correct. I wouldn't bother with it because you really have no idea if your test would be accurate or not.
The IgG is the test you need, but to get any kind of accuracy, you need to wait until 6 weeks, when 70% would show positive. Also, at 12 days you haven't had any genital symptoms. It's a really good chance you haven't been infected.