You're not alone and how you feel is totally understandable.
I am the same age as you and in peri menopause, but have not been fortunate enough to have a child (only miscarriage).
It has taken me a while to come to terms with this - especially as I no longer have a single friend who does not have children; sometimes, I feel like they belong to a club to which I'm excluded! I particularly hate the way the media assumes any woman over 35 will have children. Whenever someone announces they're expecting, I am the first to congratulate - but inside, a little part of me still crumbles.
The better news is that, over time, you do get a sense of perspective. I now call myself 'child free' rather than 'childless' which, strangely, helps. I also breathe a sigh of relief when I realise I probably won't be still paying uni fees when I am 64 (unlike some of my mates in their mid 40s with new borns).
Recently we have started the process of adoption. Have you thought about that? We're hoping to take a slightly older child. Inside, we're extremely excited, but equally, we know that it's harder than ever to be accepted, so remain determined not to feel like 'failures' if we cant proceed for any reason.
The only way I can describe it, when you hit peri, is that you will have to go through a sort of grieving process, but it does get a bit easier when you come out 'the other side' .
Big hugs x
PS Do not give up hope totally. Two of my friends well into their 40s have conceived naturally, despite thinking they were menopausal. One had three already, the other none. Both are knackered!