You should be atleast 17 years old to take up NEET entrance exam.

If you complete your 17 years before 31st dec,2021 then you are eligible or else not.

Seeing your birthday being 14 October 2004 you will complete your 17 years by  31st December, 2021.

Hence you will be eligible for giving NEET 2021.

Hello!

The eligibility criteria for NEET, regarding the age, is that the candidate should complete 17 years of age by 31st December of that year. And should not be more than 25 years of age (general category) and 30 years of age (pwd and reserved category). 

Since, your date of birth is 14/10/2004, you will be completing 17 years in 2021, therefore, you will be eligible for NEET 2021.

Hope that helps!