Can I do psychology after my BTech?

Yes. However, because the two appear to be unconnected, you must carefully arrange your career. They are, though.

A career in industrial or organisational psychology might be a good fit for you. Organisational Behaviour is a branch of psychology that investigates how people behave in the workplace and what kind of incentives may be used to boost productivity.
Organizational psychologists either collaborate with HR or conduct cutting-edge research to discover answers to people-related difficulties in work settings, since attrition, low productivity, and non-performance are major issues in today’s workplaces.

It’s a region with a lot of promise.