Eligibility for the candidature of a TGT English teacher

In any graduation course, we will have English as one of the languages. Studying this English will not give eligibility for a candidate to become an English teacher. We may not study this language in the final year of the degree course. Only those people who study English as an elective subject is only eligible for that post.
BA Literature passed students only are eligible for English teacher posts. In B.Ed English should be one of the subjects and the candidate should get qualified in CTET.
In your case, you have English in B.Ed but in your graduation, you have not studied as an elective subject. That may be the reason you were rejected.
But some institutes may take people with B.Ed with English as one of the two subjects. So when you apply for a post go through the advertisement completely and if your qualifications suit the requirements then please apply for the same.

As per your detail stated here, you have enough qualification for the TGT / Teacher in mentioned subjects as you have completed BEd / CTET with English medium. You can try as 'Fresher' for English Teacher as it needs an additional qualification (like BA English Literature for particular post).

Few months experience of English Teacher (after joining as Fresher) would help you to get the suitable job in the near future in reputed Schools or Institutes or you can continue with the same School.

Few School accepts B.Ed / CTET for English Teacher but not all. You can attend the interviews in few more schools and don't lose the hope for it. If the time permits you then you can do English literature course as well through correspondence for better prospects in English Teacher as a choice.

As far as your qualifications are concerned, it is ok for you to go in for the English Teacher since you have completed B.Ed followed by CTET making you eligible for the English Teacher.
You should keep this thing in mind that Elective English and English Literature are the two different subjects dealing with different issues. As far as I know English Literature would provide you insight how the literature developed from one era to other. You would read the works of William Shakespeare, William Wordsworth and so on which could provide you true representation of the society in those days.
Had you taken up English Literature in your graduation level followed by the same subject in B.Ed, it could have enhanced your worth.
However, you can take up English Literature Correspondence Course from some reputed institution to enhance your competence in the same subject. You should not loose hope and taking your initiatives for your improvement, would pay you dividends ultimately.

Your qualification is good for teaching field and you also tried to do everything what is required for teaching field. You have done B. Ed and CTET which is compulsory requirement for teaching field. You studied english throughout graduation but one important thing is that you should have studied english as elective paper for that post. BA literature passed student are eligible for English teacher only. Those candidate who have not studied prefered subject as elective subject in gradation are not eligible for TGT post. You also did same. You did not study english as elective subject that's s why you got rejected. But many Institute will give you opportunity for this post. First you go through advertisement and you fulfil all criteria then apply for that.

For becoming a TGT teacher in English one has to be graduate with English as one of the elective subjects and also a subject through all the 3 years. Whether you apply in CBSE school or state Govt school or KV school the eligibility is like that only. So it is clear that in your case as that eligibility is not met you would not be able to qualify for that. But there are other ways to achieve it and one of them is to go for a distance education course in graduation in English literature. That would of course eat up some of the prime time of your life but it is worth if you have a passion for becoming an English teacher. You can of course always try to become a TGT teacher in some other subject of your choice as per your eligibility.

The minimum age for the TGT English is more than 18 years and the minimum qualification is a Master's degree with 55% of marks and a Bachelor's in Education (B.Ed.). Must be trained and proficient in teaching English. Basic computer knowledge is also required for TGTs.