There are no STDs that give you a rash on your forehead.
Have you had scabies before? If you haven't, it takes 4-8 weeks to get symptoms of that. How long ago did this encounter with your friend happen?
If you had unprotected sex, you can test for gonorrhea, chlamydia, bacterial vaginosis (not an STD), yeast, and trich now - so long as it's been more than 5 days since the encounter, and it sounds like it has.
You can test for HIV at 28 days with a 4th generation DUO test.
You can test for syphilis and herpes at 6 weeks. Syphilis is uncommon in most developed countries (the US, UK, Canada, most European countries, etc.). You'd get a round, painless sore at 10-90 days (average is 3 weeks), so if you don't get that, I wouldn't worry so much.
You can get a type specific IgG herpes blood test, but please note that there are a fair amount of false positives on the hsv2 IgG test. If you get a false positive, it can take several weeks and several hundred dollars of testing to sort that out, and insurance may not cover it. If you aren't in the US or Canada, it can also be hard to access those tests.
If you don't get blisters or sores, it's reasonable to skip this test.
You could have had covid or the flu, or even RSV - all of which are actively going around now, and that could just be coincidence, and not be related to an STD.
Have a doctor look at your forehead - it's not an STD, but sounds like it should be seen by a doc.