Thanks for posting on HCM,
Well I do agree with your doctor and pharmacist that doxycycline does not cause as side effect missed period (at least in my professional knowledge).
It will be wise to start first by eliminating the most probable causes of missed period such as pregnancy
, infection (even the infection on its own can alter your cycle), pelvic diseases etc.
So there is a need to consult a gynobs who can completely examine you and request for laboratory tests and pelvic ultrasound
Ones all possible causes have been ruled out, then your doctor might decide to start investigating the unknown such as doxycycline being the culprit (missed period being a very rare side effect of doxy). Please do not rely on info you get from the internet.
Hope this helps