Doxy-1 is the brand name of a medicine called doxycycline.
Doxycycline is one of many tetracyclines and hence you will be allergic to all of them. These are Tetracycline, Minocycline, Chlortetracycline, Oxytetracycline, Demethylchlortetracycline and Rolitetracycline.
These are salt names but are sold under different brand names. For example doxycycline apart from Doxy-1 is also sold under other trade names such as Doxypal, Biodoxy etc. Hence you must read the formula of the medicine to know its contents.