JEE Main

Prepare on your own. Don't rely on any coaching institute, instead get a good internet connection and start studying online. This will be the best way to study and get the most out of your time. What you need is to focus your class 12th books Basics. NCERT textbooks are the best for IIT preparation. Just go through the books very thoroughly and then finally give lots of mock tests etc. To get a nice practice.

You can check about the college in the Shikshas college predictor. https://www.shiksha.com/college-predictor.

https://www.shiksha.com/college-predictor
Here is the link.

You have not qualified JEE exam, so I am afraid that you may not get any government college. But, still you should give it a try and I would suggest you to focus more on private colleges.

Predict the college according to your rank/percentile. https://www.shiksha.com/college-predictor

Check what colleges you can get into, use the link below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

You can check the link for college predictor. Also, if you are thinking about NIT Srinagar, then you've good chances to get in there with your rank for both EE and ECE. So, try your luck. You have fair chances.

Click on the link for more details:-https://www.shiksha.com/college/vishwakarma-institute-of-technology-bibwewadi-pune-23093

The most scoring part of JEE. Bit there is no way that you can crack the exam without preparing for physics and maths. You still have some time. Re-collect all the concepts you have learned during your 11th and 12th. And you'll crack the exam if you have formed good concepts while your studies.