B.A

Yes, you can definitely go for a Bachelor of Arts after science stream in senior secondary. You will not be denied admission to any course. You have the full authority to take the subject which kindles the interest in you.
Whether it might be literature, political science, history, economics or anything, you should give your fullest to the subject.
Generally, nowadays Bachelor of Arts stream is bit looked down. Your neighbors and relatives would say that you can enjoy for the next three years but never pay any attention to them. They are just misguiding you. Be careful!
Also, since B.A. will be a light subject compared to core courses, you are more likely to have more free time, but never ever waste them. Use them effectively to increase your skills and knowledge.
Spend most of your free time in the library reading those books which interest you, you can also join some extra classes for learning new things like Photoshop, Graphic Designing, etc.
If your parents allow you, go for some part-time job in your locality so that you can earn for your higher studies or you can prefer work from home also but don't fall prey to the scammers. There are thousands of them waiting for you.
Or if you are interested, start preparing for your civil service exams and other government exams which demand a degree as your qualification. Start preparing for those exams as soon as possible as you have a high chance of clearing it.
At last, what I would like to say is, whatever you are planning to do, just give your full efforts to it. Just don't waste your precious time and your parent's money.

If you want to come on the track which leads you to the Psychologist then thisll be your process to reach to your destination:12th with Psychology as a subject (Generally, if you want to pursue B.A. In Psychology or B.A. (Gen) with Psychology as a subject then majority of the Universities require Psychology as a subject studied at 12th standard). B.A. (Hons) in Psychology or B.A. (Gen) with Psychology as a subject. Then perform your M.A. In Psychology. Now, finally take license from American Psychological Association or other similar Psychology organisation. That's it, your now a valid Psychologist and can start your own business or join Hospitals etc.