Yes me , i got this symptom around 2 years into peri , it’s plagued me on and off every since I’m on hrt but it’s not stopped it happening no other medical reason as to why, ive had a lot of tests done over the years .
The way you describe it is how I feel as In it’s not enough to pass out but i almost feel slightly drunk like I’m swaying but I’m not , my first experience of it too was when I was out shopping.
I don’t have any words of wisdom only empathy and to let you know it’s definitely in my case a menopause symptom.
By all means do get checked out by your GP it could be an ear problem but for me that was ruled out .
Take care hope it disappears and never comes back for you x