I understand your freakout but to me it seems like you're in fine shape - and that we are in a very similar boat.
I am also applying for Classical Art/Archaeology degrees, though I'm going for the PhD. I've been out of school since 2008 and am seriously insecure about my Latin, (which I had taken for years), but I had never taken any Greek. And my modern languages are not the best, only one year of college Italian (yeah, not really what programs are looking for). So, it seems to me like you having a sampling of both Greek and Latin in college is a good thing. And most programs wont be testing you on your languages right away, but rather over the first two years, so you should have some time to get yourself a tutor / rosetta stone (my plan anyway). And if in interviews they don't bring it up, don't bring it up either.
And I am also interested in going into museum work! Do any of your programs have worthwhile on-campus museums? That's definitely something to look at. Ask about museum internships that are built into the program.