I simply can't imagine dealing with a young child with these infections. Living it myself was hard enough, and I've been lucky that my kids grew up without these infections.
Best of luck and do be sure to have not only her TSH tested, but the T3, T4 and RT3/RT4 as well. You might find this thread helpful: www.healingwell.com/community/default.aspx?f=30&m=3699283
as they are discussing lab values for the thyroid.