If I were you I'd see a doctor. Assuming you picked it up two days ago, that is sufficient time for it to settle and bite. The fact that it was not engorged is not assurance that you weren't bitten. Some people catch lyme and never show a rash, although that is uncommon.
Your doctor may prescribe an antibiotic as a preventative measure.
Swamp coolers are a thing. I don't know about the physics, but they can actually cool a space if the ambient humidity is low.
Using ice water in the gadget you have will improve its performance, obviously.