I hate to disagree with a teacher, but I think she's generalizing a bit. The Christian churches are basically divided into three classifications: Roman Catholic, Protestant, and Orthodox. The Orthodox churches you'll hear most about are Greek Orthodox and Russian Orthodox. In the United States, you're unlikely to meet many Orthodox Christians — although approximately 140 million people worldwide are members of an Orthodox church, nearly half of them live in Russia and the Ukraine.
My history teacher said that if your religious denomination isn't Catholic, than you are a Protestant. Is she right?
It could be that in your community there are no Orthodox churches (unless you live in a place with a large Greek or Russian community). If that's the case, it's possible that where you live Christians are either Catholic or Protestant, and that could be what your teacher was truly implying.
Let's not forget that the word "denomination" speaks to religious bodies, not just Christianity. There are many other religions in the world. . . including Judaism, Hinduism, Buddhism, Islam, and even other Christian-related faiths (like Mormonism, Christian Science, and Jehovah's Witnesses) that might somehow correlate to Christ but have vastly different practice and beliefs from biblical and historical Christians.