Synthroid will take 4-6 weeks to build up in the bloodstream. It is not a fast-acting medication, so some patience will be required. However, to give any further advice it would be useful to know if she was tested for anything other than TSH (Free T3, Free T4 are the most useful tests).
The hypothyroidism should indeed be treated, although I wonder about the MS connection as well. I know an MS patient who over the course of many years went through periods of delusions and cognitive decline into full-on dementia. In that case it seemed very much connected to the MS. I suppose if the MS specialists said the symptoms were not connected to your mother's MS they would know more than I, but it is curious. Usually hypothyroidism does not present with such severe symptoms right off the bat, but then again if your mother was being treated with meds and suddenly stopped taking them, it could result in a "whiplash" type effect with my severe symptoms. Just thinking aloud here.
What are her actual thyroid hormone levels? Along with TSH, they should be testing Free T3 and Free T4. If you have (or can get those), please post them, so we can better assess the testing treatment your mother is getting. Be sure to include reference ranges with any labs posted, since ranges vary lab to lab and have to come from her own report.
Most of the symptoms you listed can apply to hypothyroidism, however, I'm not familiar with paranoid delusions as being a thyroid symptom. That's not to say it can't be; just that I'm not familiar with that as a thyroid issue.
It takes 4-6 weeks for the medication to reach full potential in the blood, then it may take longer for the body to readjust to having hormones again.
Do you know if your mother has Hashimoto's? If your mother has Hashimoto's, it could be that her thyroid function has simply declined to the point that she'll need periodic adjustments, until her thyroid can no longer produce any hormones (if it isn't already at that point), then she will be dependent on the medication.