i would try to nudge your way into the doc today, if at all possible, for no reason other than to calm your nerves so you can enjoy your vacation. is there another doctor you can see? if you spoke with the receptionist, make sure he/she knows that your son has an engorged tick and exaggerate the amount of time it was attached if need be.
we dealt with tick bites a couple of weeks ago, and from our experience, there are two thought camps: treat with antibiotics at the first sign of engorgement, or wait it out and treat with antibiotics only if there is a fever or rash. if your son was older, he could take a one dose treatment of doxycycline, but because he is three, he would need a longer course of amoxicillin (can't remember if it's 10 or 20 days). we personally decided to wait it out for our three yr old, but his tick was only attached for 12 hrs or so. i also had a tick, probably on for 72 hrs, and it was engorged, but both doctors i spoke with said to wait it out as well. i actually didn't agree with this, but it turned out i got strep throat and was put on antibiotics anyways.
lyme disease is SCARY! if the tick had been on my son for 24+ hours, i probably would've demanded the antibiotics. i'll have to look up again the percentage that come down with flu-like symptoms, but it's not 100%, and only 80% get the rash. then again, after a tick bite, there's only a 2-3% chance of coming down with lyme (in a high risk area) but i don't know if i buy that, either. it's a conundrum, for sure. good luck!
Jean, feminist mama raising three boys: W (7), E (5) and L (2.15.13)