Should I have my 14 year old and 5 year old tested for Hypothyroidism?

I am 37. At 23, I was put on medication for hypothroid after having my first child. My levels were crazy, the doc asked me to stop taking Synthroid to get a clean slate. It was found that I didn't need the medicaiton any longer. It was never established if I had hypo before getting pregnant. Now 37, I finally went to the doctor after feeling HORRIBLE for many many months. (37 yo that felt like I was 70). This disorder, disease or whatever has ruined my life in recent years and I am beyond excited to finally figure out that I need medicaiton to make me feel normal again. I am now concerned about my two children. My mother and aunt both have hypothyroidism, I have it and my oldest daughter exhibits some of the symptoms (but it could also be that she is a teenager who is depressed and sleepy all the time). How common is it that children have it? Am I being paranoid? I know it's better to be safe than sorry, and I am going to take them anyway, I just wanted some opinions. Thanks!