Dear Aspirant

Yes you can shift your course and college. You can study BDS in private colleges this year and prepare for NEET alongside for NEET 2021 for next year . Previously there was a rule that one candidate can seat for NEET for only 3 times and the age limit was 25 years for general category and 30 years for other categories. But the maximum attempt rule has been revoked. So you can appear for next year NEET easily. Try hard to secure good ranks in next year to avail government dental colleges.

Check here further

https://medicine.careers360.com/articles/neet-number-of-attempts-and-age-limit

Predict your chances here

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer

Best Wishes.