Hello Jatin, 

First of all congratulation for performing well in your exams. With the rank of 37000 in JEE MAINS in OBC category you won't get NIST. You have very little chance to get admission into IIIT-D and DTU. Yes you have to compromise your branch if you want to take admission into these 2 colleges. You may get CIVIL or MECHANICAL in one of these college.

I hope you will find my answer helpful. 

All the best.