Hello aspirant 

As your NTA score is 86.05 percentile and you haven't mentioned your category of eligibility. For general category cutoff percentile is 89.75 , for OBC category cutoff is 74.31 percentile, for SC category cutoff is 54.01 percentile and st category cutoff is 44.33 percentile.

If you have qualified jee mains , you are eligible to write JEE advanced.

To get information on college that you would get refer 

https://engineering.careers360.com/jee-main-college-predictor?utm_source=C360&utm_medium=qna&utm_campaign=jee-main-college-predictor

All the best.