GP's know very little about thyroid issues. Or, I should say, they understand very little about it.
Never believe a "fine" blood test result is the best advice to anyone feeling low, tired, cold, fatigued, miserable, taking a long time to recover from exercise etc. etc. You need to get a print out of the result and research the result. There is a "normal" reference range but it's too wide. It goes up to 4.5 yet people in America are considered hypo with a reading of 3. Then in the UK they leave us until our TSH number reaches 10 before we are given any medication. You really have to fight for it. Many people can't get out of bed with a TSH of 10.
Medichecks do good thyroid panel tests. I use them and many others too. But you really need your TSH, Free T4 and Free T3 plus Total T4 at the same time. Your GP probably only tested your TSH, which is a pituitary hormone and lags behind actual blood activity. It an also be completely wrong for various reasons. Doctor's have forgotten how to diagnose thyroid issues by symptoms and by looking at patients.
The loss of oestrogen impacts the adrenal glands which try to keep the body going themselves. That impacts the thyroid gland, which slows down to ease the adrenal stress and the slower thyroid then impacts the adrenal activity and production of sex hormones. It's very much a hormonal cascade and it breaks at menopause. If you pick it up fast and get on some HRT and thyroid meds if necessary, the consequences can be reduced fast. But most of us suffer too long and do ourselves more serious harm that then takes longer to recover from.