Hello dear, 

The eligibility for NEET goes as follows: 

• The candidate must have passed class 12th or equivalent with physics, chemistry, biology/biotechnology and english as core subjects in both class 11 and 12 from recognised board. 
• Candidate should not be more than 25 years of age. 
• No limit on the number of attempts. 

So yes, you can give NEET without pursuing B.sc.  

All the best!