Thanks for the query to H.C.M. Forum.
F S H is a hormone which is produced by Anterior pituitary
T4 & T 3 are secreted by thyroid
Any disease in thyroid will increase or decrease the levels of T 3 & T 4.
In my opinion constipation
don't effects the function of thyroid gland.
However T 4 or T 3 high or low may cause many symptoms.
Physical examination by a physician will find out the exact nature of thyroid, so consult a physician.
Hope I have answered your question.
If further any question I will help.