Do you know the exact result(s) of the TSH and Free T4, along with reference ranges?
Typically, if TSH is low, Free T4 would be high but when both are low, we have to suspect Central, or Secondary, hypothyroidism. This happens when the thyroid is working okay, but there's a problem with the pituitary gland not producing enough TSH to encourage the thyroid to produce adequate hormones. Many doctors miss Central hypothyroidism because they only concentrate on TSH and if it's "in range", they think everything is fine.
The bottom line is that hypothyroidism is hypothyroidism and needs to be treated, no matter what the cause.
It will be more helpful once you post actual results with reference ranges.