To study in a Government Medical College of either Karnataka or Maharashtra or for any other State for that matter, you should apply for All India Counselling. Going by that, with a score of 560, your rank might be approximately between 19,000-22,000. This is an expected 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:

• Datta Meghe Sai Medical College, Wardha
• Koppal Institute of Medical Sciences

Apart from this, you might have decent chances in Deemed Universities in both the States. 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