Does doxycycline contain penicillin in it?

nope.

Doxycycline is an antibiotic, which is from the class of Tetracyclines.

They are broad spectrum antibiotics which mostly have to avoid dairy products, antacids, aluminium, calcium, iron, magnesium and zinc salts to prevent poor absorption of Tetracyclines (except Doxycycline & Minocycline for dairy products are unaffected)

other examples includes: Democlocycline, Minocycline, Tigecycline