I took doxycycline for a tick bite. now my period is late is that normal?

Maybe.: You could have period irregularity because you took antibiotics, or because you were sick, or because you got bit by a tick, or because you were worried about being sick, or because you are pregnant, or for other myriad reasons. Finish the antibiotics, keep a menstrual diary, and report the changes to your Family Doc in a couple of months if this irregularity persists.

NormalWithDoxycyclin: Doxicycline is known to delay periods in some women for few days to several weeks