Hello aspirant
It seems difficult to get bds seat in private college too ,with All India Rank 552712.
It is because it depends upon neet cut off. Neet cut off keeps changing every year.  It is determined by certain factors including number of students who appeared in Neet exam,  difficulty level of exam,  seat intake,  performance of the students and previous year's cut off.
Neet cut of 2024 is very high.  For general category candidate it is 50th percentile ie score between 720-164.  For sc, st and obc category candidate it is 40th percentile ie score between 163-129.
You may try for state quota seat in your state .

For college prediction you may visit the link given below
https://medicine.careers360.com/neet-all-india-college-predictor