Hi

You don't need to worry at all , you are all good as NTA doesn't send admit card to anyone you have to download it yourself .

Now , that you still have time left for your neet examination I'll suggest you to focus on your preparation and go through mock test paper sample papers and previous year question papers of neet as it will let you know your preparation level and and weak areas so that you can work on them and perform well in your examination.

Also , in addition to your neet admit card you also need to carry following documents along with you to your neet examination centre

* Your  passport size photograph

*A valid ID proof of yours like Aadhar card or Voter ID or Passport etc

*PWD certificate (if applicable)

For details go through

https://medicine.careers360.com/articles/neet-exam-day-guideline