Subclinical hypothyroidism is just a category they use for patients who do not meet their requirements for treatment. The only patients identified for treatment by TSH are those with overt hypothyroidism. All other types are basically ignored. It is unfortunate that doctors rely almost totally on a test for TSH, because it has only a weak correlation with the actual thyroid hormones, and a negligible correlation with the most important indicator of thyroid status: signs/symptoms typical of hypothyroidism.
I know it is difficult to evaluate for symptoms with a 3 year old, but see if there are any others you can identify. Also, you should get tests for the actual thyroid hormones: Free T4 and Free T3. IF the doctor resists, you should insist on those and don't take no for an answer. When that info is available, please post results and reference ranges shown on the lab report and we will be happy to help interpret further.
Also, if you want to better understand about all this, and be better prepared for further doctor visits, click on my name and then on my personal page, scroll down to my Journal. There you will find the following link to a paper I co-authored.
https://thyroiduk.org/further-reading/managing-the-total-thyroid-process/
Please be sure to insist on testing him for the actual thyroid hormones, Free T4 and Free T3. Don't take no for an answer. Very important to know. After the doctor approves I would even confirm with the lab person drawing blood that those are to be tested. You'd be surprised how often they operate on auto pilot and don't check those.