Your son is under medicated to have TSH so high while taking 175mcg and should request a dose increase. FT3 is good but that is probably due to TSH flogging the thyroid and conversion.
The goal of Levothyroxine is to restore the patient to euthyroid status. For most patients that will be when TSH is 1.0 or lower with FT4 in the upper range. FT4 needs to be in the upper range in order that sufficient T3 is converted. Read Treatment Options in thyroiduk.org.uk/tuk/about_... Email louise.roberts@thyroiduk.org.uk if you would like a copy of the Pulse article to show your GP.
Thyroid peroxidase antibodies are positive for autoimmune thyroid disease (Hashimoto's). There is no cure for Hashimoto's which causes 90% of hypothyroidism. Treatment is for the low thyroid levels it causes. Many people have found that 100% gluten-free diet is helpful in reducing Hashi flares, symptoms and eventually antibodies.
There's no advantage in waiting to correct low folate and low vitD. The sooner your son starts supplementing the sooner any symptoms due to low folate and vitD will start to improve.
To fell well our FT3 must be at the high end of the range. Often, when people are on synthetic t4 medication our bodies do not produce or convert the t4 in into t3. This is why many people who are on synthroid do not do well on it. Adding t3 is needed if ft3 levels are not optimal.
Try cod liver oil for natural source of vitamin D. Look up Seeking Health for forms of folate. Many of us cannot take folic acid.
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