Hi

No, there will be no problem at all .

This is because,

Your date of birth is not checked and is not required for Neet counselling . It is your class 10th certificates which are referred for the purpose of checking your date of birth. So you don't need to worry about your date of birth certificate at all what matters is your 10th certificate and class 12th certificate

You will need only following documents for Document Verification for neet counselling:

*your NEET Admit card
*your NEET Rank Letter /score card
* provisional Allotment Letter
*your Class 10th mark sheet and certificate
* your class 12th certificate and mark sheet
*your 8 passport size photographs
* your photo id proof ,like aadhar card or pan card or passport or driving license
* your caste certificate ,only if it is applicable
*pwd certificate ,only if it is  applicable

For detailed information go through

https://medicine.careers360.com/articles/neet-counselling

If have any other doubt then you can always reach us to clear them :) we are always available to help you out and guide you

Thank you