Hey,

The All India Counseling and the state counseling has their own dates of counseling. The state counseling usually happens after the All India Counseling as the seats which remains vacant in the All India Counseling are reverted back to state for its 85% quota.

You can surely sit for All India as well as  your respective state counseling. It won't cause you any kind of trouble.

I have attached a link below containing ALL India Counseling information,

https://www.google.com/amp/s/medicine.careers360.com/articles/neet-counselling/amp

You can refer to it if you want to know about the All India Counseling schedule.

Hope that helps.

Thank you.