Hello,
NEET is not compulsory for BSC Nursing course.

There is separate entrance Examination for BSC nursing in different universities and colleges. You need to appear for the entrance exam .
Entrance exams are conducted by universities for BSc Nursing:
AIIMS - BSC nursing Admission Test
AFMC - Armed forces Medical College
Nitte University Bangalore - NUPMET
Banaras Hindu university - BSC nursing test
PPMET - Punjab para Medical test for BSC nursing
CMC Ludhiana- entrance test for BSC nursing.

Hope this helps

Thank you