Hi @"Debbie J" I was diagnosed with Hashimoto's in 2003 after my daughter was born. I was prescribed thyroxine immediately, 50mcg, then 75, finally settling on 100mcg daily. I saw an endocrine specialist to do all this.
Hashimoto's is quite common and everyone I know who has it takes thyroxine. I would be asking your GP why you haven't been prescibed any. There may be a good reason.
My cancer treatment did not affect my hypothyroidism to my knowledge.
Good luck, and let us know how you get on. K xox