Hello aspirant, first of all congratulations on getting 97 percentile. At this percentile your AIR will be around 30K and you cannot get non core branches in NITs but you can easily get core branches like mechanical, electrical, civil, metallurgy etc. in many NITs.

You can get ECE and IT branch in IIITs like IIIT Bhubaneshwar. You have not specified your home state but you have a chance of getting IT, electrical or mechanical in your Home state NIT. You can get mechanical in NIT Patna, Civil in SVNIT Surat. You can also get Electrical  in top GFTIs like BIT Mesra.

For detailed list of colleges try this college predictor - JEE Main College Predictor 2021 : Predict Colleges based on your JEE Main Rank (careers360.com)

BEST OF LUCK!!