Can't remember what dosage I started on, as was been on it so many years prior to the cancer. Was stable on 150 for a few years. Just before surgery, had gone from 175 to 200.
I shed some hair when I was hypo, before I started getting treated (again, years ago). Not enough that my hair looked thin. Mostly, it was dry, along with my skin -- went through boodles of hair conditioner and hand cream/ I believe you are correct that hair dryness/thinning should only occur if your dose is off.
As for testing between times, it takes 4 to 6 weeks after any increase in dose for the blood levels to get up to where they should be. So, if you test it prior to that, it's not going to give you an accurate assessment of whether the dose is adequate or too much.
That said, where I live, they have a health fair deal where they run 20 or 30 blood tests for $20, including a full cholesterol panel, glucose, liver function and TSH. I'm on medication for a different condition that carries a risk of Type II Diabetes & metabolic syndrome, so I do the full health fair panel twice a year. Also be aware than when your TSH is off, it can mess with your lipids (cholesterol & triglycerides). You might check to see if your community has any comparable program.
When I first read your message, it didn't register with me how recent your TT was. I was coughing for a while afterward. Speaking voice came back fairly fast, but couldn't sing for at least a month. Everyone seems to heal a little differently, but some coughing and voice issues at this point is probably not unusual and will likely resolve themselves. No guarantees, but probably too soon to worry. Get some rest, take care of yourself and give yourself some time to heal.