Since you have not gone a full year without a period, I don't understand why they want to do a biopsy. Seems overkill. The lining typically gets to ~16 mm when still menstruating so you are well under that. Also the FSH your previous doctor did to check your menopausal status cannot diagnose menopause since it typically fluctuates between premenopausal/reproductive and menopausal range during the perimenopause timeframe when cycles tend to get irregular.
May be time for another new doctor?