According to your neet marks your rank will be around 6 2507 - 69529 according to previous years analysis , as for private colleges you can get admission into private colleges with this rank keeping generalised view of private college acceptance through neet scores (though i would be able to give a better analysis if you provide me details of state you wish to apply to) also you can use following tool for detailed analysis of colleges you can get into with this rank/marks

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