I've read from a few researchers that if you find a tick, just start taking the 21 day antibiotic course right away regardless - even if the thing just dug in.
You'll feel it itching after it digs in. Just be vigilant in the shower and use a loofa or other abraisive scrubber. Fingernails work perfectly fine as well.
Of the literally thousands of ticks I have had to remove over the years, probably less than 5 were ever left on for up to 48 hours. Most people will scratch them loose accidentally.
I went to the ER once to have a tick removed. I felt absurd doing so, but I simply couldn't reach it properly, and I had no one else around to take care of it.
Baby ticks can still carry Lyme, and can infect you with their bite.