Hypothyroid, low natural killer cells - is there a link between the two?

Good evening,

I am new to this forum, here is my background...
For years I have been going to my obgyn to find cause of monthly cycle issues. Finally the dr tested for thyroidism, and the TSH levels came back high - hypothyroidism.

Sent to another dr who has prescribed me with one dose of Levothyroxine and steadily increased it as my TSH levels would get better but then would start to rise again. When asking her what causes the thyroid to start to fail, I got the (what sounds like) typical vague response of "no one really knows what causes hypothyroidism".

My aunt recently sent me a book that has been very enlightening - I am now on an elimination/provocation diet to see if the hypothyroidism is linked to a food intolerance. I also asked my dr to run a new batch of tests - she has humored me and run the tests. I got the results back yesterday and she now wants me to see an immunologist. It turns out my natural killer cells and absolute nk cells are low. Having hypothyroidism, with everything I have read I would expect the opposite - that my natural killer cells and absolute nk cells would be too high (which would indicate Hashimoto's). One interesting note, my TSH levels are lower then before - testing against the functional range (not lab range) I am actually .1 point below the functional range now (still on the elimination diet).

Has anyone heard of a link between natural killer and absolute nk cells being low and the thyroid?

one thing I do know that in my experience is that TSH can vary wildly depending on your health status