Hello Sam, 

Observing your All India Rank in NEET UG 2019 & Score you have better chances for BDS concerning your category, too.  As you haven't mentioned your state, heres the list of state quota which can offer you Medical Government colleges with thier cutoffs:

• Andaman & Nicobar Government Colleges with cuttoff of 421 for SC & 400 for ST category.
• Andhra Pradesh Government Colleges with cuttoff of 526 for SC & 455 for ST category.
• Assam Government Colleges with cuttoff of 446 for SC & 436 for ST category.
• Bihar Government Colleges with cuttoff of 487 for SC & 486 for ST category.
• Chattisgarh Government Colleges with cuttoff of 435 for SC & 414 for ST category.
• Goa Government Colleges with cuttoff of 454 for SC & 446 for ST.
• Gujarat Government Colleges with cuttoff of 492 for SC & 478 for ST category.
• Haryana Government Colleges with cuttoff of 455 for SC & 423 for ST category.
• Delhi Government Colleges with cuttoff of 508 for SC & 482 for ST category.
• Himachal Pradesh Government Colleges with cuttoff of 437 for SC  & 412 for ST category.
• Jharkhand Government Colleges with cuttoff of 429 for SC & 401 for ST category.
• Karnatak Government Colleges with cuttoff of 552 for OBC, 422 for SC & 402 for ST category.
• Kerala Government Colleges with cuttoff of 422 for SC & 407 for ST category.
• Madhya Pradesh Government Colleges with cuttoff of 448 for SC & 419 for ST category.
• Maharashtra Government Colleges with cuttoff of 432 for SC & 403 for ST category.
• Manipur Government Colleges with cuttoff of 522 for OBC, 398 for SC & 373 for ST category.
• Mizoram Government Colleges with cuttoff of 419 for SC & 400 for ST category.
• Odhisa Government Colleges with cuttoff of 422 for SC & 400 for ST category.
• Puducherry Government Colleges with cuttoff of 420 for SC & 400 for ST category.
• Punjab Government Colleges with cuttoff of 453 for SC & 418 for ST category.
• Rajasthan Government Colleges with cuttoff of 462 for SC & 425for ST category.
• Tamil Nadu Government Colleges with cuttoff of 417 for SC & 401 for ST category.
• Telangana Government Colleges with cuttoff of 542 for OBC, 422 for SC & 430 for ST category.
• Tripura Government Colleges with cuttoff of  422 for SC & 402 for ST category.
• Uttarakhand Government Colleges with cuttoff of 442 for SC & 416 for ST category. 
• Uttar Pradesh Government Colleges with cuttoff of 439 for SC & 407 for ST category.
• West Bengal Government Colleges with cuttoff of 424 for SC & 406 for ST category.

Here's  a link which would help you more for getting admitted to Medical  Government College through State quota:

https://medicine.careers360.com/articles/neet-cut-off-for-government-colleges

BEST WISHES!

Hii Sam

To know whether you will get admission into government college or not two things play a important role:

1)The state you belong to

2)The category you belong to

Since you have not mentioned your state it would be difficult to say about the colleges,but yes you have a chance of getting government medical or dental college.

Thank You