There are surely many headache triggers, and you don't state much about your situation (do you have Lyme, how long
have you had it, is this your first time treating?).
In terms of Lyme disease and adverse reactions to antibiotics, there is the Herxheimer Reaction. It is fairly specific to Lyme disease, though also (and originally, I believe) observed in syphilis. In a "Herx" reaction, the die-off of the bacteria causes a worsening of symptoms, or sometimes even new ones.