Yep don’t forget to thoroughly degrease/wash every article of clothing that you wore on the day of exposure!
I’m sure you’ve already extensively searched desperately for info on salvation (as I did when I had a gnarly poison oak rash) - but just in case, the rash itself is not contagious and there’s nothing to rub off after the initial exposure absorbs into your skin.
Also as others have said, calamine lotion is a lifesaver for the recovery phase. Highly recommend, available OTC at most pharmacies.
If you have access to medical care, a syringe full of fexofenadine is what my doctor gave me upon seeing my weeping limbs so maybe you could ask for that as well! My rash was very stubborn and refused to heal, continuing to weep for weeks until that shot cleared it up overnight. It’s possible you are similarly allergic to poison oak (like, more than normal, actually allergic) if your rashes don’t clear up.
On the bright side, I had such a large area exposed that I’m now mentally immune to itching so I guess that’s cool to look forward to. Hang in there!