Yes, You are eligible for NEET 2019, As per the eligibility criterion a student must be at least 17 Years of age as on 31st December 2019, So by simple calculation a candidate born before 1st January 2003 is eligible to appear for NEET 2019, Since You satisfy the eligibility criterion You are eligible to appear for NEET 2019.

As per the NEET 2019 eligibility criteria, You are required to complete 17 years of age either at the time of admission or else on or before December 31, 2019. You can check teh further eligibility with the given below link.

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

Good Luck!