I am also in NY, I get ticks all the time bud and there are 2 methods I use.
1) I use a water bottle cap (or something of similar size) and fill it with dish soap or vegetable oil and flip it over on the tick so the soap or oil completely covers it. Ticks use "gills" to breath and when they can't breath, they release and drown in the liquid. Water does not seem to work for some reason, I am assuming it's because there is oxygen in H2O but unsure.
2) just grab that sucker and pull. I have bought all kinds of "miracle tick remover" type tweezers and none of them get the mouth out in my experiences.
A tick must bite something that has Lyme, then release, then attach to the next host to give the 2nd host Lyme disease. If a tick lays eggs Lyme isn't passed on to the young, they must latch onto something that has Lyme to get it. If you know ticks you know they don't release willingly so I am assuming they would only detach from the host to lay eggs but I am speculating there. In our situation we would kill a deer and the ticks on that deer would have to detach and then be looking for a 2nd host.
A tick has to bite and stay latched on for roughly 24 hours before it can give the new host Lyme (allegedly). I don't understand why, but that is what "they" say.