Dear Yashoda, 576 is a very nice score. In 2018, under State Quota, for OBC Category,  only 2 colleges had cut off higher than 576:

RUHS: 592

Sawai Man Singh: 596

So, you have a fair chance at these colleges, based on their previous cut offs:

Dr. Sampurnanand Medical College: 573

GMC, Bharatpur: 559

GMC, Durganpur: 560

GMC, Kota, 567

GMC, Pali, 560

Jawaharlal Nehru Medical College: 569

Jhalwar Medical College: 566

Rabindranath Tagore Medical College: 569

Having said that, cut offs change every year and are dependant on various factors like no.of seats available, no.of candidates appearing for the exam, top NEET score and difficulty of the exam. So we would suggest you to wait until the official answer key has been released to weigh your options.

Hello student,
Yes, With a score of 576 in obc category you can get a seat in the government medical colleges when comparing the results of previous years. Last year, a score of 559 was required to fetch one a seat in the Government medical college, Dungarpur in obc category under the state quota. But one thing to keep in mind is that scores and ranks vary each year with difficulty level of the question paper and availability of seats. However you can predict the colleges which you are likely to get using the given link
http://medicine.careers360.com/neet-college-predictor
Good luck

Hello student,

First of all congo for scoring such high as with this score there are high chances for you to get a seat some government medical college in Rajasthan as you also have resident quota of Rajasthan will help you grabbing good opportunities as compare to outside student.

Hope it helps. 

Thank you  :)