As your JEE Mains 2019 score is 87.5 percentile in ST category and this year JEE Mains cutoff for ST category is 45 percentile. You can definitely apply for NITs through Joint Seat Allocation Athority (JoSAA) counselling 2019. Don't worry with your JEE Mains score you can easily get NITs. Now as you have cleared JEE Mains cutoff you are eligible for JEE Advance 2019, so you can try and prepare for that hope you crack JEE Advanced too which may get you through IITs. 

Hey Naveen,

You can get a seat at any average nit like

NIT JSR

Nit Calicut

Nit kurukshetra

Nit Durgapur

Nit Rourkela

Nit Hamirpur ,etc.

You should go for branches like chemical, civil, electrical and mechanical engineering depending upon the previous year cutoff of these nits. 

You can check the link below to check the colleges that you can get this year :

https://engineering.careers360.com/jee-main-college-predictor?utm_source=google-search&utm_medium=paid&utm_campaign=jeemain-clgpd

Good luck !

Your percentile is enough for you to get NIT in ST category. If you don't get it in first time. Apply for second or third rounds of counseling. There is high chance of getting NIT for you.