Your GP is talking absolute tosh. I have a mirena so haven't had a period since I was about 35 and I've never had a hot flush. I only realised I was in Peri when I mentioned to a friend that I was becoming scatty and forgetting things/losing things and she suggested menopause. When I went and checked the symptoms I had 4 or 5 of them.I had a chat with my GP this morning because I've been very conscious of the peri thing and he actually told me that he's worried too many women are chalking things up to that at the moment, that you do need some clear signs like proper hot flushes and a year of no periods before it's worth looking at blood tests and whatnot.
Can't recommend tracking everything via an app like Clue enough; you can tag your own monthly weirdness like specific moods and pain as well as all the fairly standard issues, it really helps with keeping an eye on cycles and what's "normal" for you.
Tracking is an absolute must, even things like bowel movements and peeing change during the month. I'd recommend any woman track from puberty onwards to learn their specific signals. It really can be life changing.
ETA This isn't a Male GP issue, it's a GP issue overall. I've had Female GPs just as bad. It comes from ignorance, 1 even admitted to me that all she knew about Peri was what her patients had told her.