If you are so serious about a career in a good school, and would like to become a teacher of the science subjects, given your background, it is absolutely essential that you complete the B.Ed degree course, at least through the distance education mode. The IGNOU, and the Madurai Kamaraj University and the Bharathidasan University at Tiruchiralli offer this course.
Once your are in, you also need to complete the M.Ed course, so that you are very competitive. Remember, these days there are very smart teachers who have additional Diplomas that help them to be ahead of their competitors.
Whether you want to work in North India or even North East India, whether you want to work in Government or in a residential school, with accommodation and affiliated to the CBSE, or in a State Board School, please do remember, without the B.Ed degree nothing is possible at all. Even if some school were to appoint you, sooner or later, you will feel that you need the B.Ed degree. More so, in the Hindi belt, as every Hindiwala knows that it is impossible to survive without the B.Ed degree. Apart from this, a very command over the English language is positively insisted, even in the Government schools. Generally, it is fine and good from a career point of view that you join only an English medium school, rather than a Hindi school.
This is because, you would have already studied only through the English medium and you will find it very difficult to switch over to the Hindi medium, even if your native language is Hindi.