Magnesium supplement may help with constipation.
Lots of Hashimotos patients seem to suffer low magnesium - as well as many other low vitamins & minerals. Low stomach acid can reduce our ability to absorb nutrients from what we eat.
Also we also often have acid reflux due to LOW stomach acid. Not something I have had much...others say Apple cider vinegar helps. Or if very bad Betaine HCL
GP's often seem to confuse reflux as being due to HIGH stomach acid .....then prescribe PPI's, these lower magnesium further
The book The Magnesium Miracle is worth reading, not that it looks at thyroid...just magnesium .....or "google" obviously
It explains why Serum magnesium blood test is not worth doing - if going to test needs to be Whole blood Magnesium RBC test.
What time you take thyroxine is important, some find taking at bedtime gives better results (myself included), must be 2 hours after eating, and no food or drink other than water for hour after either.
Very important when get thyroid levels tested not to take Levo in the 24hours beforehand (take it straight after test instead) and ideally get test early in morning before/at 9am, don't eat or drink other than water beforehand (this all helps give highest TSH and help stop your GP wanting to reduce the Levo due to "TSH being too low").
Lastly Supplementing Vitamin C (with zinc) may also improve thyroid as well as constipation
If you can keep notes or a file of all your results - helps to see where you are at, what improves you etc. It is a complex puzzle and only you will understand what works for you. We are all different.
You can now access you own GP patient notes on-line, if you are in UK. Need to register first at the surgery. This gives you access to all your blood test results going right back over the years - very useful