Your FT4 is about perfect. It's 53% of range, and midrange is the guideline for FT4.
FT3 is 41.5% of range, which is actually a little low of the upper half of range guideline. However, since you are not on meds, I wouldn't consider it abnormal at all. A low TSH usually indicates hyperthyroidism (high FT3 and/or FT4).
TSH is very volatile and can change as much as 70% depending only on the time of day the blood was drawn. It's the least important of the 3 tests.
Since you have no symptoms, I wouldn't worry about the TSH at all. You might want to keep an eye on it, perhaps retesting in 6 months unless you have symptoms in the interim.
I don't think your labs or your symptoms (or more properly lack thereof) in any way warrant a referral to an endo. Apparently, your doctor has admitted to lack of knowledge in this area, and he appears to know himself well!
free t3 range 2.40-4.40 pg/mL
free t4 range 0.93-1.70 ng/dL
tsh range 0.27-4.20 uIU/mL
No symptoms and no medication.
What are the reference ranges on your FT3 and FT4? Ranges vary lab to lab, so you have to post both together.
Do you have any symptoms?
Are you on thyroid meds?