My best suggestion to you is to shift into Banking sector from BPO Sector. To get job in banking sector, you are required to appear in entrance examination (Common Written Examination CWE) which is conducted by an autonomous body Institute of Banking Personnel Selection (IBPS).
Yes, as far as my knowledge is concerned, you are right track now. Getting job in Banking sector in the present competitive world because quite tough. So for this, you must have a keen, regular and strong preparation for IBPS CWEs. To overcome the present competitive world, I suggest you to join any best coaching institute which offers banking examinations preparation. So that you will be in right track and of course you may secure top marks which are required for final selection in banking sector.
No, Bank jobs won't add pressure to your life. Here is the explanation for my previous words. See Bank timings are 10:00 AM to 4:00 PM for customer, where as 10:00 to 6:00 PM for bankers (employees) in maximum cases. So you will have to work in the said timings only, see once you selected as a banker you may work in the stipulated time irrespective of work that you are given. Unlike private jobs, you may even complete the remaining work on the next working day also except for Day End work in Banks. So everything becomes quite easy as you go on learning the new things in Banks. So I strongly suggest you to join best coaching institute and make yourself in order to overcome the present competition.