We are not experts... we are patients, who have been through similar experience...
Total T3 and Total T4 aren't the best tests to tell what's going on, but they're a start... Could you please, however, provide the reference ranges, since ranges vary from lab to lab and have to come from your mother's own report.
TSH is not a good test to give the full picture, but elevated TSH indicates that your mother is suffering from hypothyroidism.
It would be best if you could get her doctor to order Free T3 and Free T4, which are the thyroid hormones that are actually used by the body... It does appear, from what we, typically, see that your mother's levels may be very low in the ranges, which would go along with the high TSH.
This means that her thyroid is not producing enough thyroid hormones to satisfy the needs of her body. The thyroid controls metabolism, heart rate, body temperature and other body functions and when there aren't enough of these hormones, one can have many adverse symptoms.
Hopefully, her doctor has recommended that she start on replacement thyroid hormones... Please let us know the course of action recommended.