You can't really gauge the conversion unless you do the fT4 and FT3 at the same time. Yours were done separately, but don't really indicate an conversion problem.
What all of them indicate is that you're under-medicate. Your TSH is much too high, it should be under one. So, before you got wondering about T3, you should get an increase in your T4 dose, and retest in six weeks time.
If both FT4 and FT3 are low in range then an increase of Levo is the way to go, as increasing your FT4 will also increase your FT3 if your conversion is good enough. So we need to know the range for FT4.
On the face of it there doesn't seem to be anything wrong with your conversion. Good conversion takes place when FT4: FT3 ratio is 4:1 or less. Your ratio is 15.8 : 4.1 so 3.85 : 1 so that doesn't point to needing T3.
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