Hey Himanshi!

With 488 marks in NEET 2019 ,you are surely eligible for counselling. For getting information about the counselling process of NEET , you can follow the given link :

https://medicine.careers360.com/tags/counselling-of-neet

And Based upon your score in NEET 2019 i.e. 488 and the previous year cutoff, chances are less for admission to Government Medical Colleges under All India Quota. You may have chances for admission to colleges under state quota. Use NEET College Predictor to Check Your  Chances in All India Quota, Deemed Universities & State Quota seat Based on Your NEET AIR
https://medicine.careers360.com/neet-ug-college-predictor?icn=neet-clgpd&ici=qna-answer

Hope it helps!