Yes, if you are hypothyroid, you often have an early menopause - and if you have an early menopause, you are often hypothyroid.
It certainly sounds as if you are experiencing the menopause and if you are suffering from low oestrogen, the dryness will make you more prone to UTIs. Were you getting on ok with the vaginal pessaries?
I started on systemic HRT properly a year after my last period. I tried it before then, but it was hard to get the level right as my own hormone levels were still fluctuating wildly.
Do you have an appointment soon with your own GP?