MRI scans aren't that bad. I had one done on my head, twice. Or was one of them a CAT scan? Either way, your strapped to a board and sent into a tunnel that makes a rumbling noise for a few seconds to a few minutes and then its done. It doesn't hurt at all.
Can you ask for something to help relax you? When I was in the MRI machine they had a music system set up so I could listen to that while the machine hummed and rumbled about me. It was very soothing to have music to listen to and I almost fell asleep. I even got to choose and bring in a cassette tape to listen too (it was a very long time ago that I had my MRI done ).
Surgery isn't as scary as you think. The doctors are usually very nice and accommodating, and they can explain what every machine they are hooking up to you does and what every IV line is for. Its a little daunting to think that they are going to open you up and preform a surgical procedure on you, but they are only doing it to make you healthy.
I come from a family of medical practitioners (grandma was a nurse, and aunt is a nurse though not currently working due to personal reasons and cousin and her hubby are doctors), and have had to deal with hospitals more so than most people (baby brother was hospitalized for Acute Lymphatic Leukemia) so it doesn't bother me at all, like it does some people.