Hello and welcome to the forum
TSH levels are not the cause of hypothyroid symptoms, they are an indicator that the thyroid system has a problem.
TSH (Thyroid Stimulating Hormone) is made by the pituitary gland and is produced to tell the thyroid 'you need to make more T4 and T3'. A healthy thyroid gland responds by doing this and the TSH level quickly falls as the pituitary is satisfied.
The true situation is more complicated and you can read about it here: http://en.wikipedia.org/wiki/Thyroid-stimulating_hormone
TSH testing is well established and is easier and cheaper than the tests for other things like T4/T3 levels which is why the NHS and GPs like to use it for managment of hypothyroidism especially. They can see the TSH level gradually go down as T4 medication satisfies the pituitary gland. (The body can convert T4 into T3 as needed - usually - but that can be a different and separate problem).
Hypothyroid symptoms are caused by a lack of T4 and T3, but the TSH test results are a simple and cheap way of monitoring progress. This is fine for 'simple' hypothyroidism where the cause is failure of the thyroid gland. If the pituitary gland is not producing TSH in a normal way (for whatever reason) then TSH monitoring is of no use.
You don't mention T4/T3 test results in your posts so I assume your GP is not having them tested?
If I was showing these symptoms and TSH variations, I'd want an endocrinologist to have a good look at me and I'd want lots more tests with T4/T3 just to start with. Please ask your GP to do T4/T3 tests and seriously consider asking for a referral to an endocrinologist.
I'm not saying all this to alarm you but to emphasise that TSH testing is just the start of understanding thyroid related problems. I hope we can hear some good news about your partner in the future.