There is much to discuss, but first I am not clear about you being diagnosed with Graves' , but then you mention testing for antibodies. What tests were done and what were the results compared to reference ranges? Also, I don't understand how an ultrasound can show the presence of Graves'. For example note this info in the following link. "Our findings indicate that sonography has high specificity but low sensitivity in the diagnosis of either Graves’ disease or Hashimoto’s thyroiditis. It is therefore not possible to differentiate between these two diseases using sonography alone. Confirmation by laboratory data is also needed."
Why didn't the doctor just run a TSI test for Graves'? Seems like it could have been postpartum thyroiditis, rather than Graves'. That would better explain the hyper followed by a hypo phase you are going through.
Next thing to note is the whoever ordered your tests did not do the right ones. The Total T4, T3 Uptake and Free Thyroxine Index are outdated and not nearly as useful as testing for the biologically active thyroid hormones, Free T4 and Free T3. Since the correct definition for hypothyroidism is "insufficient T3 effect in tissue throughout the body due to inadequate supply of, or response to, thyroid hormone, there are a number of important variables that affect response. Those include Vitamin D, B12 and ferritin. So you need to also get those tested and then supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper part of its range, and ferritin should be at least 100.
Along with that, in order to relieve the hypo symptoms you have, you need to increase your med dosage as needed to raise Free T4 to at least mid-range, and Free T3 into the upper third of its range. What dosage of NP Thyroid are you taking daily?
Another important thing to note is that in the future you should defer your morning dose of thyroid med until after the blood draw, in order to avoid false high results.
Most important of all is to have a good thyroid doctor. By that I mean one that will do the necessary testing and then medicate you adequate to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results.
One grain of NP Thyroid is not going to be nearly enough for you. The average daily output of natural thyroid is 100 mcg of T4 and 10 mcg of T3, which equates to 130 mcg of T4. The 130 is equivalent to 2 grains of NDT like NP Thyroid, and that doesn't take into account the loss from lack of absorption of the med. So the expected amount of replacement NDT is 3-5 grains. Of course everyone is different and gets different results. That is the reason that thyroid med should be adjusted as needed to relieve hypo symptoms, without creating any hyper symptoms, rather than based on test results only, and especially not TSH. Since you are limited in resources for testing I would start with Free T4 and Free T3, and Vitamin D and ferritin. When you have additional test results please post here and we will be happy to help interpret and advise further.