Hi

Ofcourse, you should take part in All India counseling.

496 is a good score to take part in All India counselling. You may get good government College till second round of counseling.

NEET UG counseling schedule has been announced, you can check it on NTA official site and mark your dates

ntaneet.nic.in

For prediction about colleges via your rank and marks, please refer to this link-

https://medicine.careers360.com/neet-college-predictor?utm_source=qna&utm_medium=neet_cp

Best of luck