Dear aspirant, for a better clarity you can check out the college possibility for your score in the link mentioned below.

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer

Good luck and proceed accordingly. Last year Siddharth medical College and Rajiv Gandhi medical College general cut offs were 588 & 583 respectively. Still in the later rounds there is a possibility you can get a seat in a reputed government college.