Can I get admission in MBA or in another professional degree or in medical field after completing B.Sc in zoology, botany and geology?

If you want to do MBA, the criteria is that you should be a graduate with 50% marks. So, if you completed your B.Sc then you can write entrance and join for MBA. The chances of getting a job in the medical field is a bit difficult as compared to getting an MBA seat.

Yes, you can pursue MBA or any other course of your choice after B.Sc.