JEE Main

No chance of getting CSE with this rank:

First of all, admission in IIT is based on your JEE Advanced rank, not on the basis of the JEE Mains score. Second thing is that if your SC rank is below 10-12K, then you may get a seat in NIT or in GFTI.

With 88 percentile, it's not possible for you to get admission in any of the NITs or top government colleges. So, it's better to go with private Institutes. As you see in NITs, the seats are less than 600, for a student whose AIR is more than 10K cannot get admission in any of the NITs.

Kindly visit this link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Kindly visit this link:
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjttrm95qHiAhXd8HMBHUdwD_0QFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Kindly use this link:
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjttrm95qHiAhXd8HMBHUdwD_0QFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Yes. As you have got 97.05%ile in JEE you are competent enough and eligible enough to apply for it and to secure admission so go for it and apply.

To know which colleges you are eligible for, use the college predictor tool:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

No, It's not possible for you to get admission in any of the NITs as the seats are limited to less than 600. So, those who get AIR of less than 1400 will get seats in NITs. I suggest you to go with private institutes.

You should participate in your state engineering counselling.
Best of luck.