You haven't mentioned the reason why you need to update your Aadhar card. But the Supreme Court did mention that Aadhar Card is not mandatory for educational and employment pursuits. So for NEET exam, it is not mandatory that you need to take your Aadhar card. You can carry a Valid Id proof such as your Voter Id card, Driving license. Your Passport, Ration Card are also acceptable. Your Valid id card for proof  that you take for examination hall should be issued by the Government of India and is a permanent once. Also take 2 recent Passport size photographs.  And if you are preparing for NEET, you may as well try our NEET Knockout package: https://learn.careers360.com/knockout-neet-may/ . And because you have 2 more months to prepare for NEET, you may as well use this opportunity