Sorry to hear that you're in for a TEE. I had to undergo one of those a little while back while my docs were trying to confirm a diagnosis of constrictive pericarditis. Of course I did not want to undergo the test, but my cardiologist explained that this test offers some of the best physiological views of the heart....
It sort of sounds like maybe you've had one before, though? If so, then best wishes to you; if not, I can assure you that the test is really not all that bad. It's just like heartangel says---they practically knock you out, and the whole thing is over before you know it. The worst part for me was when they were putting that goop in the back of my throat, in order to numb it. You'll do fine, though!
Really, the TEE was among the least of the things I had to endure (the bone marrow biopsy, angiogram/catheterization, thoracentesis, and, ultimately, surgery were all a great deal worse than the TEE.)