I am glad that you have reached out and also have the self awareness to bring about a change to bring about some happiness and contentment in your career choice and life..
We spend almost 3/4th of our time working.. and if that is not giving is any satisfaction then this dis-satisfaction and unrest spills over in every other aspect of our life as well our emotional well-being and eventually our health.
You have 6 years of IT experience and that will help you to seamlessly take forward in the NGO sector.
For a job in the NGO sector please look at : http://www.devnetjobsindia.org/
For Jobs in teaching, you can look at either doing this course that will give you an entry into international schools : http://www.itari.in/ITARI-CIDTL-AD-Aug2016.pdf
If you are looking at colleges- then you will have to do your post graduation and apply for a Mphil...a post graduation is enough to apply for the college job in the private universities.. with application for an Mphil
For PSU and government jobs- giving the GATE exam.. also the UPSE etc will help.
it would be a good idea to come online for a chat session so that we can take this forward and make it more tailored and specific to your interest and your career goals.
All the best!