Hi - now that I know I was in the process of my ovaries failing for all of the last year, I can confidently share my opinion that if you have symptoms of anxiety regardless of whether your GP is 'listening' to you about your own intuition and wisdom re peri menopause please focus on the anxiety.
I have had a tendancy to anxiety most of my life but have always managed it myself and usually only been really challenging during big life changes but......in the past 2 years it has got much worse and quite different from how I had experienced it before and none of my usual 'talking myself down' rationalising the issue helped. I did not know what the issue was for a start - it was just out and out fear.
My GP did and still doesn't not take this into account, so the cynical me says that you will need to find what works for you on this front unless you want to try medication. I started with a routine of learning to breathe properly, using phone apps or other guided excercises were really helpful for me, calm.com has 2/5/10 minute sessions with positive focussed themes. I approached it lightly, just added a couple of 5 or 10 minute sit downs a day to start with - taking this time out and growing confidence to know what calm feels like in my body has really helped. Despite the random days - mostly first thing in the morning where I can feel scared and anxious and adrenalin fueled, I mostly remember that at some point I will return to base.
Aside from finding your own little relaxation, focussed breathing time (could be stretching or yoga type things) I also have regular accupuncture. Again, it gets me into balance and reminds me of my 'higher' wisdom head and not the fearful one - I do sleep better after too.
For me, the anxiety and all the heat symptoms remain reduced if I am calm, so I focus on this key area as my stabalising point. I also try and drink plenty of water and stay hydrated. Stress hormones will increase inflammation in the body and just generally make everything 'heat' up and whir around - this hormonal 'storm' is really something - I had no idea! In my calm moments, I like to think it is an opportunity to come to a place where one no longer feels so overwhelmed by out of control feelings or situations.

I do believe if I had known that I was experiencing perimenopausal symptoms and understood this affected my anxiety I would not be in such a challenging place right now. I thought I was going mad or some other physical illness was coming upon me & generally felt overwhelmed as I didn't have a grip on what I was dealing with. So now I choose to strengthen the anxiety management part of my life and hope to god the rest calms down.
Saying all that, I had 4 hours sleep last night and a terrible morning anxiety wise - but, it passed and I had accupuncture and felt back in touch with myself.
I haven't read any books - I can't seem to read/focus much at the moment