When making the switch from T4 to a desiccated type med, patients often feel better for a short while because they are still getting the effect from the old (higher) dose of T4, and adding T3, which is faster acting then T4. It is kind of unusual that you would feel worse on day 2; however, the problem you face is that your new dose is not even equivalent to your old dose.
Conversion tables erroneously show that 100 mpg of T4 = one grain (60 mg) of NDT = 25 mpg of T3. When you examine it closely it makes no sense because if 100 mpg of T4 = 25 mpg of T3, then the ratio is 4 to 1. So if you take 60 mg of NDT, which contains 39 mpg of T4 and 9 mpg of T3, and convert the 9 mpg of T3 to equivalent T4, at a ratio of 4 to 1, then the result is 39 + (9 times 4) which only equals 75, not 100 mpg of T4. In addition there are two studies that have shown the ratio should be closer to 3 to 1 instead of 4 to 1. So the AACE/ATA Guidelines for Hypothyroidism says that it should be 3 to 1.
Thus, if you convert 60 mpg of NDT to equivalent T4 using the 3 to 1 ratio it comes out to be only 66 mpg of T4, which is far from the conversion apparently used by your doctor. So just to maintain the same effect you would have been placed on two grains of NDT, which would be 120 mg. In addition you said you still had symptoms with the 137, so I expect that you need more than the two grains.
A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results. So I suggest that you first make your doctor aware of the correct ratio of T4 to T3, which is shown in the second paragraph on page 1002 of the Guidelines in this link.
ATA/AACE Guidelines for Hypothyroidism in Adults, Endocr Pract. 2012;18(No.6)
Then you should request that your dosage be increased to the two grains that would be close to your old dose of 137 mpg of T4. Then after you are stable on that dose you can see how it affects your symptoms, and if you need more med. When taking thyroid med, dosage should be adjusted as needed to relieve hypo symptoms and by monitoring Free T4 and Free T3 feels. Typically Free T4 needs to be around the middle of its range, at minimum and Free T3 in the upper third of its range, or as needed to relieve symptoms.
Since hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferritin, I would also request tests for those as well. D should be about 55, B12 in the very upper end of its range and ferritin should be about 70. After testing you can supplement as needed to optimize.
Not usually. What med and dosage were you switched to?