Menopause certainly can cause heightened anxiety. The couple of years around mine my anxiety was far greater. The time where the problems are worst is in the peri-menopause, the period leading up to the cessitation of periods.
The age at which Mother, Grandmother experienced menopause is generally taken as an indicator. You could ask your Doctor to do an FHS blood test which will show the levels of hormones and whether this could be part of the problem.
That said, panic can start as swiftly as you describe, nothing one day and then bang. It did with me.
Hope you manage to find out.