Can a thyroid problem cause skin to become sensitive to touch?

Thyroid and skin: This is not a common complaint of a thyroid disorder. If you were hyperthyroid (eg. Graves), you could be "hyper" all over, and I can imagine that could be manifest as skin sensitivity. If your thyroid level is normal (i.e. taking thyroid replacement) then these symptoms are probably not thyroid related.

No!: Thyroid problems can cause some skin changes due to slowed metabolism. This may include dry skin and some facial swelling(under active function) or excessive sweating ( if over active)