With 582 marks in NEET in general category you can get the following states in Kerala under the state quota. The below cutoffs are based on last year marks and are expected to rise this year because the exam was comparatively easier this year and students are performed better. Although the exact rise in cutoffs is difficult to estimate and hence colleges with scores like 579 could go out of your range this year. Hope for the best all the best

T D Medical College, Alappuzha-552

Government Medical College, Ernakulam-568
Government Medical College, Kottayam-579
Government Medical College, Manjeri-558
Government Medical College, Thrissur-569

If you go through previous data , you can observe a score above 550 is always the safest score to land into a good MBBS college in India. And I must say 582, you have done a brilliant job. You must apply for counselling, and wait to get a seat in a good government college. 

~All the best!

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