So can hashi's raise the white blood cell count? I've never been tested for it. But the last CBC I had my white blood cell count was on the verge of high. It was like 9.5 out of 11. I didn't have any infection that I was aware of.
It sounds to me that you need to have a thyroid ultrasound done. Have you had one in the past? Sounds like your thyroid is goitered.
If your free t3 is low and your reverse t3 is high, then you should probably be on a low dose of T3 meds. Are you on any meds now?
Where is your free t4 level at?
Any autoimmune disease can affect your white blood cell count and the rest of our immune systems since they are in over drive from the antibodies.