When I first started having problems and went to an ENT, he sent me for a CT Scan and an MRI as he suspected an AN. My CT Scan came back clean, no sign of anything. The MRI (without contrast) showed a 1.8cm AN!
If you or your ENT suspect you may have an Acoustic Neuroma, you should absolutely have an MRI to confirm or rule it out. If you do in fact have an AN it's better to find out, know the size of it and what your options are. AN's don't go away like a virus and this is not something to ignore based on a fear of having an MRI.
While MRI's are challenging for people with claustrophobic issues, they are manageable. You can take Ativan or something similar to help relax you. I personally do not like confined spaces, so I always have a soft cloth placed over my eyes and request the lights in the machine be dimmed. I focus on my breathing and try to imagine what the sounds I'm hearing in the machine remind me of. It helps make the time go quickly. You have a button to hold in your hand if you need help at any point and you can speak with the technician. There is nothing in the machine to hurt you and it is totally non invasive, so that should help calm you somewhat.
Hopefully others will post and give you further info about different types of MRI machines available. I believe there are some places with "open" MRI machines where you can stand up, but I'm not personally familiar with them.
Best of luck!
Cathie