Hi, Hope you are safe and doing good

No,passing the MBBS is a pre-requisite for being considered for a PG seat in Psychiatry. So,it means without a MBBS degree you cannot be a Psychiatrist.

But, definitely you can become a psychologist. For that you need to complete your Bachelors and Masters Degree in Psychology. And typically, you need to do an internship for couple of years.
Psychology deals with behavior of a person an psychologists can apply their finding knowledge to a lot of services.

And, after getting your degree and completing your internship you can be hired as a Clinical Psychologist or as a Counselor. Not only this,you can also be hired as an Industrial or Social Psychologist .

Hope it helps
Feel free to ask if you have any query
Thank you !