Welcome Community

Hi there. If you still have your ovaries, no, you do not go into menopause. You will experience that when the time comes....normally around the age of what...47 on up.....
I also had a hysterectomy for fibroids when I was 43, I'm now 47. What most women don't realize, as a LOT of them don't even know their own body or the female reproductive system (NOT to say that you don't....really.) is that when you keep your ovaries your are still 'ovulating' each month but you're just not having periods. Which is sooooo nice now. I still get my usual 'monthly' headaches that I used to get with my period. I'd get them about 3 days before my period was due and as soon as I'd start, it would go away. Still the same without the actual period, LOL.
Anyhow, if it were me, I'd make absolutely sure the doctor did not take the ovaries, too. You really should not be experiencing symptoms of menopause IF you still have your ovaries and they are working properly. I'd assume if they weren't working properly, they would have removed them. So far I have had no symptoms of even starting perimenopause or premenopause.
But, I was a smoker. WAS. I did find that I would get hot and cold! For me, I was smoking toooooo much, LOL. I stopped smoking several years ago with the help of nicotine gum. I got hooked on that and got off it by exchanging every other piece with actual chewing gum. I would suggest cutting back, at least, if you are a heavy smoker like I was.
And yes, some if it can be healing...........
I hope this helps! Take care.....