First of all, It's an achievement to score this much in NEET exam. There are different factors which decide that whether you the government college or not.

1. Your category

If you are General category student so 560 marks may not enough for All India quota. But you may get a seat through state quota. Last year the All-India quota cutoff for general category students was 610-630+ for top government colleges.

If you are OBC candidate cutoff was slightly low 590-610, but still tough to get a government college in All India quota.

If you are SC/ST category student, then you will definitely get a government MBBS seat in both All India quota and state quota.

2.Type of Quota

State quota: 85% seats are reserved for the domicile students, if your state has a good no. of government colleges then there are more chance to get there.

All India quota (AIQ): Only 15 % seats are there for non-domicile students.