Hello Deepti

Firstly, as per the NEET UG 2019 eligibility criteria, candidate should have studied Physics, Chemistry, Biology/Biotechnology  and English as core subjects in both Classes 11 and 12th from a recognized board and have scored 50% minimum aggregate marks in PCB subjects for UR category and 40% in case of OBC/SC/ST category.

As mentioned, you have studied Physics, Chemistry, Biology and if you have the required aggregate marks in PCB then you are eligible to apply for the NEET exam.

However, you must clear your compartment exam of Mathematics.
Good Luck!

Yes private candidates can be eligible for NEET 2019 who have compartments  

However you should get it cleared before Counselling for NEETUG  

Eligibility criteria sharedbelow for NEET 2019.

https://medicine.careers360.com/articles/neet-eligibility-criteria/amp