Hey,
Well,it is generally not allowed to take handkerchiefs in the NEET examination. You are basically not allowed to carry anything except the hall ticket and ID proof. Having said that, in case,you are not well and really need to carry handkerchiefs so you need to take the permissions of the officials present at the centre of your examination. The last decision is theirs.
For detailed information about the dress code of NEET,follow the link given below:
https://medicine.careers360.com/articles/neet-dress-code
Hope this helps.
Good luck.

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