Hello,
As you have mentioned that your neet score  is 359 marks and you fall under general category. Let me tell you that the NEET cut off varies from year to year, state t state and as well as college to college. It also depends on the Quota you are applying through as well as the Category of Admission. Government and Private Colleges have cut-offs of their own.
Assuming you are applying through the 15% All India Quota under general Category for a Government Medical College, the cut-off for NEET 2018 was Rank 10000 which corresponds to a score of approximately 540+ marks out of 720.
So, looking over this scenario your chances to get seat seat for mbbs is private medical colleges is almost negligible.

You can check out the expected private medical colleges as per your rank/marks using the link below:

https://www.careers360.com/college-predictor

I hope this would help you. For further queries please feel free to write me down in the comment box.

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