Prednisone has a long half life (lasts longer) than Cortef or Hydrocortisone (generic for Cortef). Many take Prednisone as a replacement. It has to be converted in the liver so takes longer before it is available for the body to use.
Hydrocortisone is like what a normal body makes. Cortef & Hydrocortisone have different fillers so some of us do better on one or the other. I don't do well on Cortef.
5mg prednisone would be a min replacement dose for addisons/adrenal insufficiency. 7.5mg is the max dose. Taking that much for over 4 weeks would tell your adrenals they don't have to work. Was the prednisone tapered at the end of the treatment?
Yes, prednisone is one of the cortisol replacements used to treat addisons/adrenal insufficiency. Actually the one I prefer, but I use hydrocortisone as it is like what a normal body produces. Prednisone has more anti-inflammatory benefits & is used for many things.
I'm not a doctor, so my opinions are just "opinions". You still need to rule out adrenal problems if you have any of the symptoms.
Are you having symptoms other than being tired?
Did you actually see the results of your thyroid check? We are often told things are normal when they are not. Good idea to get copies when you have bloodwork done so you can refer back to it at any time.