Hello there,

Hope you are doing well . Firstly Congratulations for such a great score in NEET 2021 . With a score of 631 I expect your AIR is something about 7.9 to 8.2 K. See ,for now it's difficult to predict the exact cut-offs as they change every year depending on various factors . But we can predict your chances of getting admission into different colleges depending on last year cut-offs as it is expected to be somewhat same to NEET 2020 cut-offs .Since you specifically asked about Rajasthan , here is a list of colleges that you can get through State quota counselling in Rajasthan for OBC quota :

1) GMC, Bharatpur

2) GMC, Dungarpur

3) GMC, Bhilwara

4) GMC,Pali

5) GMC,Churu

6) GMC, Barmer

You can check the NEET 2020 cut-offs through the link given below :

https://medicine.careers360.com/neet-college-predictor?utm_source=qna&utm_medium=neet_cp

As for your 2nd question , yes if you are getting a government medical college be it old or new just go for it . The academics and clinical exposure tend to be good in all government medical colleges and rest depends on your own hard work after you get into the college .

Hope my answer helped .