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from the info you provided - falling always to one side points to several possibilities:
1. weakness on the side to which you are falling - something along the lines of "my knee buckles and i fall"
2. problem with balance center peripheral (ex. inner ear) - responsible for balance
3. (most likely( problem with cerebellum - center of the brain which is responsible for maintaining balance and coordination (ex. stroke, acoustic neuroma)
the first thing you need to do is to see a neurologist - he/she can differentiate between above possibilities (may require MRI of the brain and ENG - dizziness/balance test)
medications side effects is also a big possibility - need to review your meds and see if anyone of them can cause this.
2 blood pressure meds may predispose you to "orthostatic hypotension" - rapid drop of BP and increase in heart rate with rapid changes in position - 20 points drop after getting up fast is enough to pass out or fall.
your doc may do BP measurements lying down and standing, but tilt table test would be more specific.
the fact that you were taking same meds without adjustment for a while now makes it less likely, but still possible.
I was not suggesting that it was orthostatic, but with info you initially provided it could have been a possibility.
I often see mri reports with similar interpretations - white matter disease could be this or that or whatever - most often it is neither........ these are signs of chronic ischemic changes likely blood pressure related....... very unlikely MS.
going back to your initial question- you started having symptoms 3 months ago, mri was done 2 years ago........ if any of these "white matter ischemic changes" occur in your cerebellum - it would give you the reasons for falling. I would suggest to repeat MRI.