Yes, you may definitely give NEET, while pursuing B.Sc. Many students perhaps do this, when they fail NEET or fail to secure a Medical Seat in First Attempt. You may join a B.Sc. Course preferably in a Relevant Domain like Botany/Zoology or Chemistry or maybe Physics and parallely prepare for NEET UG for the upcoming year.

For more information about NEET Preparation do follow the link below

https://medicine.careers360.com/articles/neet-preparation-tips/amp