MS is just a lousy disease.
Your problem with sweating does not necessarily have to be a result of the medication. You may have a lesion in your spinal cord. They often affect the autonomic nervous system.
I suffer from the opposite. I have not been sweating at all for years. As soon as the sun shines, I overheat and get tired. If I’m not careful, I get a fever. For me it is a consequence of the lesions, because I do not take any medication. And I was told by the doctors that excessive sweating in MS is much more common than not sweating at all.
When I researched what I can do to make myself sweat again, I noticed that there is no information about it but for the opposite. Many people with pathological sweating are treated with Botox.