I had similar results as yours when first diagnosed. I'm fine now.
You need an increase and the aim is to bring TSH to around 1 or lower. Some Endos are happy if it is somewhere in the range but most of us would not feel well. Your total T3 is too low but the two tests which inform us most is the Free T4 and Free T3 blood tests but few do these.
The aim is a TSH of 1 with FT4 and FT3 towards the top of the range. The most important is how the patient 'feels' on particular doses.
I shall give you a couple of links - the first to read about FT3 and FT4.
Blood tests have to be at the very earliest, fasting (you can drink water) and allow a gap of 24 hours between last dose and the test and take afterwards.
Levothyroxine should be taken on an empty stomach with one full glass of water and wait about an hour before eating.
Most members take levo when they awake and some take theirs at bedtime, if bedtime dosing you should have last eaten about 2.5 hours previously. Food interferes with the uptake.
Ask doctor for B12, Vit D, iron, ferritin and folate as everything has to be optimal.