Dear Betsy...
Don't worry about getting fixated in one therapy. It's like learning anything - if you keep dotting about, you'll never learn how it can be used properly. William Webb Ellis may have "invented" Rugby, but that's no way to get good at football.
Plus, CBT is so rich, so diverse, you may as well worry about feeling claustrophobic in the open air as worry about getting fixated in CBT!