All of my sx initially were right side. Slowly I felt things over to the left (especially the feet tingle thing).
BUT: New symptoms appearing on the opposite side of your body should be at least reported to the Neuro. Left sided issues involve the right side of the brain and visa versa.
When I started getting symptoms on the opposite side, my doc ran a new MRI to check for new lesions.
Sometimes we already have lesions in different parts of the brain that start acting up but are not really "new".
My advice: Report it to doc and let him/her decide.