Hi there... I have a few questions to ask, if you don't mind.
Do you have your RA under control? Can you, please, tell us what symptoms you have?
What type of anemia do you have - iron deficiency or Pernicious Anemia (inability to absorb vitamin B-12)?
You're correct that, both, your TSH and Free T4 are low in their ranges. Typically, with hypothyroidism caused by a thyroid defect, we'd expect TSH to be much higher than it is, with FT4 so low. With them both low, we have to suspect Secondary or Central hypothyroidism, which is when the thyroid works fine, but there's a problem with the pituitary/hypothalamus axis, in which the thyroid isn't getting enough TSH to stimulate it to make adequate thyroid hormones.
Many doctors fail to diagnose Secondary hypothyroidism, because they dwell mostly on TSH and as long as it's "in range", they think all is well, when that couldn't be further from the truth.
Next time you have labs, ask your doctor to add Free T3 to the order, as well. Free T3 is the hormone that's used by almost all the cells in our body, while Free T4 is considered a storage hormone and must be converted to Free T3 prior to being used.
Even though Secondary hypothyroidism is suspected, you should ask to be tested for thyroid antibodies to rule out/confirm Hashimoto's, which is an autoimmune thyroid condition that erroneously considers the thyroid as foreign and produces antibodies to destroy it. Since you already have one autoimmune condition (RA), the chances of getting another (or more) are greater.
The antibody tests you need are Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb).
If your doctor doesn't suggest that Secondary hypothyroidism, you should suggest it to her/him, in order to be sure it gets looked at.
Also, I am not on any thyroid meds and never have been. Thank you!