Hi,

The neet registration portal is open upto 24th june. So yes if your score is above the qualifying marks then you can definitely apply for neet counselling.

However one thing to be aware of is that the all india counselling is held for 15% government seats and for deemed university.

With your rank its difficult to get a government college both for mbbs and bds. 

Your options available are deemed university or private college. 

If you want to try for deemed then its counselling is held similtaneously with the15% AIQ counselling. Register for it and fill your choice of deemed university wisely. You stand a chance of getting a seat.

However if you want private college, then its counselling is held along with the 85% state quota counselling and you need to have a state domicile if your the college doesn't have open seats.

So under neet counselling you can apply for deemed but not for private. 

I shall attach a link which can be of help:

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