Thanks for writing in.
Thyroid disorders tend to run in families. So given the fact that both you and your husband have a thyroid condition, your daughter may be prone to developing it too. However, since you say the thyroid antibodies are both negative, the chance is less but sometimes underactive or overactive thyroid problems can occur without detectable antibodies in the blood tests.
Now you have raised a good point about the diagnostic considerations ie thyroid versus pituitary. In order to fully interpret the thyroid laboratory tests that you have shared here, we need more tests. I would recommend repeating the TSH, Total T4 and do Total T3 with T3 resin uptake along with prolactin. There is no need to fast for these tests and they do not have to necessarily be done in the morning.
Anemia can occur in 'hypothyroidism' but if the thyroid turns out to be normal then evaluation of the hemoglobin status requires an independent work-up.
Endocrinologists are the best type of specialized doctors to competently manage these complex test results.
Hope that this information helps and hope that you will get better soon.
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Dr. Shehzad Topiwala