With a score of 566, your rank might be approximately between 16173-19478 . This is an expected All India rank range: https://medicine.careers360.com/articles/neet-result-marks-vs-rank . Now regarding the Colleges that you may have a shot at, you have a chance in:

• ACPM Medical College
• Ashwini Rural Medical College
• BKL Walawalkar Rural Medical College

Having said that, this is based on 2019 data and cut offs change every year. Cut offs change every year depending on various factors such as no.of Candidates appearing for the exam, no.of Candidates qualified, top NEET score and difficulty of the exam. For a complete list of colleges that you may have a shot at, please use our College predictor: https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer