Dear Sushil, last year score of 560 secured seat in Government Medical College, Dungarpur under STATE QUOTA in GEN category.
At 581 you have a fair chance of getting seat in GOVT medical college under STATE QUOTA.
Here's the list of Medical colleges whose cut off was less than your score -

• Dr Sampurnanand Medical College, Jodhpur-580
  
• Government Medical College, Bharatpur-563
  
• Government Medical College, Dungarpur-560
  
• Government Medical College, Kota-569
  
• Government Medical College, Pali-563
  
• Jawaharlal Nehru Medical College, Ajmer-576
  
• Jhalawar Hospital and Medical College, Jhalawar-567
  
• Rabindra Nath Tagore Medical College, Udaipur-579
  

Also, since the exam was bit easy this year so the cut offs are expected to increase.
You can check the given below link to predict your college other than those metioned.
https://medicine.careers360.com/neet-college-predictor
All the best.
Feel free to ask for any query.