Dear aspirant!

No, you can't become a gynecologist just after completing the BAMS. To become a gynecologist you need to complete MD  or MS in Gynecology. for Gynecologist the minimum degree requirement is MBBS so you need to pursue PG after BAMS from ayurvedic college. You're not eligible for pursuing MS Gynecology course offered by Allopathic institute and corporate hospitals.

hope it helps!

good luck!