Hope you are doing well. Yes obviously there are  low chances for you to get government seat for veterinary with 361 marks. In obc category you need score 360- 400+ in 85% state quota.

Since you didn't mention the name of your state it is difficult to predict college.

Although getting government seat for veterinary depends upon various factors like number of students appeared in the exam, category, region, AIQ rank, state, state rank, etc.

For more information you can visit NEET College Predictor

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

I hope this information helps you.

Good Luck!!