This looks like a developing (yet mild) subclinical hypothyroidism -- if is has been going up every three months, it is likely a progressive thyroid problem. Hashimoto's thyroiditis would be the most
commonCommon cold explanation. Would see a pediatric endo. At this point the numbers are slightly abnormal (provided that the
T3 of 446 is in the reference range for that lab) and should not be putting him at any significant health risk, but he needs evaluation to help prevent worsening.