Hello, Suresh Kumar Pandey

It will be difficult for me to say you will get a government college or not because cut off varies from year to year depending on difficulty level category home state etc 

However 550+ is a score when you feel safe you will get a government college and you have score 516 you have a slight chance of getting admission in government college 

I'm providing you a link which can help you

https://medicine.careers360.com/neet-college-predictor

Hope this helps you if you have any queries you can add in comment section

All de best