Grecomania is a modern, made-up word combining "Greco" - an anglicized word meaning "Greek"- and "mania", an ancient Greek word meaning madness and passion.
Grecomania probably evolved as a companion to Egyptomania, which was first coined as a word during the first King Tut fervor which erupted in the early 20th century, which denoted a similar passion for all things Egyptian.
The more sedate term meaning much the same thing is "philhellene" - one who loves and admires all things from Hellas, the word the Greeks use to describe their own country. The first "philhellenes" were well-educated students of ancient Greek philosophy and ancient Greek democracy. In more modern times, passionate philhellenes such as the English poet Lord Byron went to Greece to fight on the side of Greece against the Ottoman oppressors - Byron lost his own life doing so, and he continues to be venerated as a hero of Greece.
If you want to cure your own Grecomania, you can try getting it out of your system by planning a trip to Greece. But don't count on it. Most victims of Grecomania tend to get worse, not better, once they've seen Greece and the Greek islands.