Would talk to your surgeon about that, typically they are not removed. But if they are the clear cause of pain, it may be worth considering.
Thyroid imbalance can influence the nerves.
It is best to keep TSH in range (0.5-2.5) and also continue to look for other more common causes by seeing a neurologist.
Would see an endocrinologist for general evaluation including cortisol (adrenal) testing.
Certainly making sure the TSH, T4 and calcium levels are normal would be part of that.
A TSH of 4, even w/ Hashi (high TPO) does not require treatment. Usually TSH >10 requires definite treatment. So if not tolerating meds, then consider a trial w/o.
However a high(ish) TSH may promote goiter growth....this is one consideration in deciding on treatment.
The TSH levels look okay.
Would consider non-thyroid causes - perhaps a rheumatology evaluation
Thyroid consideration would be combo T4/T3 treatment (ie, add cytomel) but this only helps 10-15% of patients in our experience.
The high TSH means HYPOthyroidism. This may be part of the overweight problem. Would test TPO antibodies as w/ this family history, it is likely Hashimoto's despite the "normal" thyroid on ultrasound.
Treatment is with levothyroxine to bring the TSH back to the 0.5-2.5 range.