My thyroid hormone levels vary over the years. So testing is an on going process, and nothing is written in concrete for the rest of your life. I have always been on the generic, and have never had any issues using it. I would get the test, and make whatever adjustments are necessary.
If it is only being tired that is your issue (you are able to stay warm and maintain your body temperature) I would also get a sleep study done. A very high percentage of those treated for head and neck cancers have undiagnosed sleep apnea, I was one of them. It was waking me up 20+ times an hour if you can believe that. I was tired mid afternoon unlike anything that I had ever experienced. Ingrid joked that I was just becoming like Barkley, our old dog that sleeps his afternoons away, and that chronologically (dog years considered) we were about the same age. I am still struggling with controlling my apnea, and it is still a major problem.