6mm is pretty tiny - as in the size of a pea. I am only a layman - but my guess is that it is likely benign given the rounded appearance.
Double vision can also be indicative of things like myasthenia gravis. I have no idea about MS - there is a forum here that covers that. The tumor could be a factor, but it depends on location and I am not good enough at telling exactly where this is and if this location would cause tremors and all. It could be that you have a combination of issues. I know in my case, I had multiple issues and it made it harder to diagnose.
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