Hi your thyroid problem will not pass on to your child , as for you i guess you will have to continue medication for a more longer time as indicated my your doc with a necessary blood check of every 6 months to know your levels. however if your child is suffering of constipation and nose block or irritation etc pls ask your doc to do an intestinal check for both of you sometimes there may be bacterial infections in the intestine which cause allergies and prolonged back aches and constipation and hormonal changes weight gain etc. Thxs and take care. bye all the Best.