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I live right next to East Lyme, the town where Lyme disease was first discovered, and I go for walks in deer and tick infested forest every single day.
I'll tell you right now you have zero chance of having Lyme. First of all the tick needs to be attached to you for approximately 3 days before it can transfer lyme disease to you. Sounds like you removed it pretty quickly. Secondly, only 3% of ticks have the lyme bacteria.
As for the rash, it takes about 1 week to show up, however sometimes you can get lyme disease with no rash. Still I wouldn't worry about it. Just remember to check yourself after going for walks next time.
