I think you should get a second opinion from a different GP or change GP. You should have been prescribed Levothyroxine when your TSH was >10 which is overtly hypothyroid. Under 10 is subclinically hypothyroid but should still be treated if the patient has hypothyroid symptoms.
Carpal Tunnel Syndrome is a classic hypothyroid symptom which often resolves without surgery when optimally treated with Levothyroxine.
Aching muscles and low mood can also be signs of vitaminD, ferritin, B12 and folate deficiency which are common in hypothyroid people. Ask your GP to do blood tests. If they are deficient NHS should prescribe supplements but if they are low in range you will need to self supplement. Post your results with the lab ref ranges in a new question and members will advise.
I agree completely with Clutter's response. Carpal Tunnel is also a symptom of hypothyroidism. Whoever is treating you needs to be sacked from caring from you as they have no knowledge whatsoever of how to treat people with hypothyroidism. If you can delay your op for CT (I myself had the syndrome but didn't need an op as it was remedied without having one). Get a GP who knows how to treat you and increase your levothyroxine your pain may diminish.
email louise.warvill@thyroiduk.org and ask for a copy of the Pulse online article by a doctor who was President of the British Thyroid Association and question 6 is self-explanatory. Your GP has to give you sufficient hormones to reduce your TSH to 1 or below. I would rather you saw another doctor as the one you're seeing now appears to be ruining your health.
Having an op for CTS is a difficult decision - but I would be inclined to wait and see what happens when you are being treated for your Thyroid. There is a great deal written about CTS on this forum - so type it into the Search Box on the Green Bar above and you will be read about others experiences/ideas.
You may also be LOW in B12 - when this is low it can affect the myelin sheath that protects the nerves in the body. When this is compromised you will experience nerve pain - especially in the very narrow area of the wrist.
Oh crikey. You need some thyroid meds! I was assumed to have carpel tunnel. Could hardly use my mouse at all at work. Had health and safety and GP involved. Was then diagnosed hypo started on Levothyroxine and the pain in my hand, wrist arm went as quickly as it came. You need a different GP as soon as possible. Good luck and I hope that you get some help soon xxx
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Understanding blood results
Latest Results,
Latest Results 
Latest blood results (on T3) teva
Latest results. Very upset :(
