JEE Main:  There is no age limit to be eligible for JEE Main 2019. However, candidates need to pass 10+2 or the equivalent examination in 2017 or 2018. Candidates appearing for 10+2 or equivalent exam in 2019 are also eligible to apply irrespective of their age. Since you have passed out in 2016,you are not eligible for JEE Main.

NEET: Please cross-check with your Date of Birth.
Minimum Age Requirement: 17 years as on December 31, 2019. Candidates must be born on or before January 1, 2003.
Maximum Age Limit:  Not more than 25 years of age for unreserved category candidates and 30 years of age for reserved and PwD category candidates (Case pending before Supreme Court; final criteria will be notified with the release of NEET application form 2019)

AIIMS:  Candidate should have attained 17 years of age. There is no upper age limit for AIIMS Entrance.