Hi again, sfgirl,
Current wisdom is that it takes only 24 hours (and possibly less) for a tick to transmit Lyme disease. There isn't universal agreement on this, so you'll see various points of view being expressed on the internet (and elsewhere). The longer a tick is attached, the greater the chance of being infected.
The nymphal ticks that usually infect people do so because they are so tiny and usually cannot be felt. That's said, it IS possible that your rash is something other than Lyme disease, however as momtomonsters has pointed out, almost anyone who has (or has had) Lyme disease would be looking for 21 days of doxy just to play it safe. Trust me, it can be a devastating illness if left untreated or only partially treated.
Gotta go, but I'll check in later.
Hope this helps a bit.
Rita