With a score of 556, 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:

• Maharaja Agrasen Medical Collge
• Maharishi Markendewar Universty
• ESIC, Faridabad

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