Thanks for the useful information which will help me to clarify with the doctor.
A TSH of 10.54 indicates hypothyroidism. However, TSH is, at best, a screening test, which should be considered with more important tests, like FREE T3 and FREE T4, and symptoms.
In an of itself, a TSH of 10.54 is not alarming. My TSH was in the 60s on diagnosis, and we hear of people with TSH in the hundreds ocassionally.
I would suggest that you ask your doctor to test the actual thyroid hormones FREE T3 and FREE T4. These will give you a much better idea of what the thyroid is actually doing. Be sure your doctor orders FREE T3 and FREE T4, which are different from total T3 and T4. Bear in mind that FT4 often has to be midrange and FT3 upper third of range before symptoms are relieved.
There's a good possibility that your wife has Hashimoto's thyroiditis, which is an autoimmune disease and by far the most prevalent cause of hypo in the developed world. Antibody blood tests would confirm this: TPOab (thyroid peroxidase antibodies) and TGab (thyroglobulin antibodies).