It wouldn't hurt to call ahead and ask exactly what to expect (believe me, you're not the first claustrophobic person!).
I had a bad experience, personally, with my head one because they didn't tell me that they were going to have to screw down what felt like a Hannibal Lector type plastic mask over my head so that I absolutely couldn't move it at all. I'm also overweight, and they literally had to pull the blanket tight across my shoulders to wedge me in (I had my eyes closed, but know that I was in past my elbows, and this was for a head MRI). They then switched techs partway through without telling me and when I called out, no one answered me for a second, which really freaked me out.
Honestly, I swore I would never go for another one, but....
Since then I have gone to a large city near me to an "open" MRI (which isn't really, but is at least better), and have had nothing but bearable (not positive, but not screaming mimi either) experiences.
I always ask for pillows under my knees (because of my bad back), extra blankets (because it always seems to be freezing), and for them to turn up the music REALLY loud through the headphones

. I also ask that they talk to me, keep me informed as to how many minutes, how many more scans, etc. It might also help to ask "when" you can wiggle even a toe for finger, because you will start wishing you could, even though you shouldn't!
Good luck, I hope the drugs help, and that the findings are worth it

.
Terri