Many people have had great luck if not better luck on Armour Thyroid. I understood this to be natural Thyroid but somehow pharmaceutical grade. While it is derived from pig thyroid, the variability I think seems less than many would fear.
I'm not sure if "raw" Thyroid is OTC, but my understanding is that Armour Thyroid required a prescription.
You could, but what is the point? If you need more T4 or T3, why not get your doctor to prescribe FDA approved meds. The concern is that OTC thyroid meds may not be as closely controlled for quality and consistency. Since thyroid levels need to be fine tuned to achieve adequate symptom relief, I would always want the Thyroid hormone content in my meds to be very consistent and predictable.