Hello student yes you can find your Neet application number easily by following the steps mentioned below -

Tap on the link - https://ntaneet.nic.in/ntaneet/online/GetCandAppno.aspx

Now fill all the same information which you've have filled in the application at the time if submission

Then fill the security pin/Captcha

And Submit, after that you'll get your Neet application number. The reason it's saying errors is you might fill details wrong so please remember the details properly and then fill it to recover your application number.

For more details refer to the link mentioned below - https://ntaneet.nic.in/ntaneet/online/GetCandAppno.aspx

Feel free to comment if you've any doubt

Good luck