What is the possibility I have thyroid cancer with normal TSH levels and a solid nodule that has doubled in size in 2 years?

Depends. Each nodule has a 5% risk of cancer. Any mass that is significantly changing in size needs to be investigated. See your doctor to discuss ultrasound-guided biopsy. Tsh can be normal in cancerous nodules.
Possible . I would be concerned a bit about your nodule and would definitely have a biopsy of it done with an ultrasound guided fna. Most thyroid cancers don't affect the TSH level so that does not mean anything.