The disease comes from mice, not deer. Deer do help spread the ticks around, but reducing the deer population wouldn't significantly help with lyme disease prevalence.
I'm actually currently on roughly day 14 of doxycycline for possibly having it or some other tick infection. I got bit on the shoulder by a nymph, found at somewhere between 18 - 24 hours later still unengorged. I then got the 200mg prophylaxis later that day, meaning that my odds of getting anything should have been less than 1%.
I never developed a lyme rash, only a local rash, but my shoulder and arm started hurting within a couple days. I tried to convince myself it was just from using my laptop even though I've never had any RSI problems, or else just from being tense from worrying about it, but it was still sore on and off for the next 20 days. Finally woke up and my whole arm was burning, so I drove down to the pharmacy and had the scrip filled within the hour. It's frustrating though because there's really no way to know if you have it in the first place, and also no way to know if you're actually cured once you finish the treatment. The symptoms did go away pretty much as soon as I started taking the meds, but who knows what that really means.