Dear Shreya,

559 is a pretty decent score and you may have a good chance to secure a government medical College with the score you got. I can assist you further if you mention which state you belong to otherwise there are numerous medical College with all India Quota score less that 559 hence you may get a government medical college through that. I am attaching the link below where you can check cut off of each state and College, state and AIQ cut off and cut off of the different categories.

https://medicine.careers360.com/articles/neet-cut-off/amp

Dear candidate,
Colleges is totally depend on the marks you got and the rank. Different states have their own criteria for seats to allote. Under state quota the 85 percent reservation for state students and under all india quota the 15 seats for the other state students.

As you have not mentioned about any state, its difficult to say about any college with any information. You have chance in your home state seats.

For that here I am providing you with the link of our site portal to predict your college by just mentioning your information for the college and know you applicable colleges.

Follow the below link to predict your college:
https://medicine.careers360.com/neet-college-predictor

Hope this information helps you to get college details.  
Thank you