What you described is a hot flash.
I have been having them for over a year. At first, they were just the first couple of days of my period. Then, they were throughout my period, with other severe symptoms. Then, I started having them during other parts of the month.
My doctor tested me for menopause. (I am 40, young for it, but not uheard of.) Nope.
He also tested my thyroid level. Was 3.94 TSH results. He said it was normal.
Well, I got very fatigued suddenly at the start of one of my periods with body aches and didn't get well. Tested TSH again and it was 8.45. I have hypothyroidism.
Hot flashes are one of the symptoms because body temporature is regulated by the thyroid hormones. So, the body is having trouble doing that. And, estrogen does contribute toward that. In fact, estrogen works against thyroid hormones. That's why the fluctuations of estrogen in perimenopause cause hot flashes.
As to the other. I don't know if it has anything to do with hypothyroidism.