English Spl

English Phobia is mostly in our heads. There are no grounds for the poor performance in English. Rather, India is 4th out of 19 Asian countries in term of English proficiency.
Don't be disheartened by criticism. Work hard on academics and speaking English. You'd be surprised by the results.
Firstly, start reading English newspaper. I suggest this step to everyone I come across. This not only improves your vocabulary but also gives you a sense of being better informed. http://carryongarry.com/learn-500-big-english-words/
English will not obstruct your JEE journey. It is part of the syllabus in boards and learning language is as important as being well versed in technology or PCM subjects. But ultimately in JEE only PCM is going to get you scores and marks.
For improved English, your last step can be enrolling for a coaching. There are various Personality development coachings that work on your language and communication skills too.
It is a fun activity and I would suggest it only if you want to join one. You'd come across many people like you who are struggling with their English.