I was going to say Pregabalin and Kathleen beat me to it. I don't know how but it removes the bad feelings both mental and physically, depending on dose.
I was prescribed Gabapentin years ago and still have it on my repeat list so occassionally I order it and occassionally I take it. Gabapentin is the weaker medicine and tbh I find it too weak to do much, but it will stop me feeling down or grouchy and it might help with pains in my arms and legs but it's delayed if there is an effect at all.
I believe there are controls on the prescribing of it because they are both class C controlled substances, that's why I keep it on my prescription list, so I can show the police if necessary!!!
If you have nerve pain running down your arms or legs or in your back, then they can prescribe them and you won't have a hot flash or night sweat while taking Pregabalin, but these aren't things they can prescribe it for.
Like Kathleen says it can be prescribed for anxiety too, to me it would be preferable to a benzo for that, but they might try to fob you off about anxiety, I was told to try meditation for my menopause anxiety by my GP.
I think if you got prescribed either of those it would help, clonidine is another one that is supposed to help with hot flashes and sleep, it makes me too sleepy for daytime use. I got it prescribed specifically for menopause whereas the other two are for nerve pain.
If you have a chat with a good pharmacist, they know which medicines women keep coming back for and which ones get dropped after a month or two.