I don't know of someone and Dr Skinner is sadly missed. If you email email@example.com she has a list and there may be someone in Scotland).
I am sorry your sister is so unwell and it's good you are searching on her behalf.
First if you get a print-out of her blood tests from the doctor, with the ranges - these are figures in brackets after the result. You can then post them on a new question for comments from members.
If your sister didn't follow the procedure below which has been found to be the best for diagnosing I'd ask GP to do another blood test and tell him previous results might be skewed. Or you can get a private one from Thyroiduk's recommended labs. Some doctors won't take notice of them.
First the appointment should be at the very earliest appointment and don't eat anything before it, although you can take water.
If she was on thyroid hormones she'd allow 24 hours between the dose and the test which should be: earliest and fast.
If we eat, it can reduce the TSH (thyroid stimulating hormone) which might result in not being diagnosed or unnecessarily reducing the dose of thyroid hormone replacement (usually levothyroxine).
If the doctor only tested TSH and T4 these don't tell the whole picture. The tests should be TSH, T4, T3, Free T4 and Free T3. (T3's are important as they are the active hormone required in all of our Receptor Cells otherwise we can feel very unwell indeed. T4 is inactive and has to convert to T3. Even if 'in range' T4 and T3 should be towards the upper part of the range not just 'somewhere' which many doctors think is o.k.
Also ask doctor to test:- Vitamin B12, Vit D, iron, ferritin and folate as these deficiencies can cause problems as well.
From now on always get a print-out with the ranges for own records and so that they can be posted for comments.
p.s. some doctors believe that if the TSH hasn't reached 10 (the British Thyroid Association's recommendation before prescribing) they don't prescribe. Whereas in other countries if TSH is around 3+ they will.