Hello gunjan, 

Well according to last year's cutoff you are very close to the cutoff score. Which means you may have chances. 

Here's a link look to it :

https://medicine.careers360.com/articles/neet-cutoff-rajasthan

Don't lose hope so early. It is possible that you get a college in later counselling rounds. So apply for the counseling process as soon as the dates are announced. 

Thank you 

Hello!
Congratulations on your score! With a score of 587, you have a good chance of getting a government seat in UP. Here, I'm listing out the government colleges in Rajasthan:

https://medicine.careers360.com/colleges/list-of-government-medical-colleges-in-rajasthan

Good luck!