Have you had a recent blood test for your thyroid hormones? If not, I'd suggest you do as your last increase was in January.
Doctors usually only test the TSH and T4. That really only reveals the whereabouts of the TSH (from the Pituitary Gland) and T4 is levothyroxine but we need the T4 to be towards the top of the range. When we are quite newly diagnoed it can be quite confusing to learn about results etc.
Do you feel well with no clinical symptoms? If so that's good. Your Consultant has said that the dose you take at present is fine? I am dubious sometimes to know whether their patient is 'really' well.
As regard 'puffiness' it is also a clinical symptom maybe due to not yet being on sufficient hormones. This is a link and you will see puffy eyes is only one of many symptoms.
The following is important:
Blood tests should always be at the very earliest, fasting (you can drink water) and allow 24 hour gap between last dose and test and take afterwards.
Hormones should be taken first thing on an empty stomach with one full glass of water.
If preferred you can take at bedtime as long as you've last eaten about 3 hours before (food interferes with the uptake). If so, you don't take the night dose until after a.m. blood test and night dose as usual the same day.
Ask GP to test B12, Vit D, iron, ferritin and folate. We are usually deficient.
Always get a print-out of your results with the ranges. Ranges are important as labs differ and it enables members to comment.
Ask GP if he will request a Free T4 and Free t3 blood test. He probably wont as TSH and T4 is what is the guideline and sometimes lab wont even if requested. The reason why we only need these occasionally (if we don't feel well) and you can read in the following link why. We do have recommended labs which do tests.
Levothyroxine is T4. T4 should convert to sufficient T3. T3 is the only active hormone required in our receptor cells.
Put a short history in your Profile, of when diagnosed, with what, and dose at present.