Fungus isn't contagious, but it will infect any fish with damaged tissue. Quite often poor water quality will affect a number of fish in the tank and they develop it in the damaged areas.
Doxycycline is an anti-biotic that kills bacteria (including filter bacteria) and does not affect fungus, yeast, viruses or anything else. It was designed to treat bacterial infections in people and should only be used on fish with a known bacterial infection that has not responded to normal fish medications.
I can't tell anything from the pictures.