Call ahead and tell them you have extreme noise sensitivity, and ask if there is anything they can do to provide extra ear protection, or if there is anything they can tell you to bring to help with this problem.

Last MRI I went to have, they gave me the little foam ear plugs. And then the headphones with music over those. But at different locations, they have done much more. Especially for a head MRI, since they are putting the frame around your head and want to make sure you don't move--the foam plugs, then wedging what felt like big foam pads or sponges in each side over my ears. You will still hear the noises, but they are much more muffled that way.

To help with the claustrophobic feeling, I always have them put a washcloth/towel over my face (first time I ever went for one, they offered, so now if they don't, I ask). Then you don't have to worry about keeping your eyes shut while you're in the machine, or seeing how close the top is to you.

And if you are worried about the claustrophobic thing, no need to be. While it is narrow inside the tube, remember that it is completely open at both ends, they can slide you back out at any time, and you are not far in at all. Relax and enjoy the rest. Instead of being annoyed by the noises, I try to imagine them as the beat of different kinds of music, or make up a story around them (like voices arguing) (okay, so I'm weird. but I have actually fallen asleep and take a short nap during some.)