Due to excessive dust which made me extremely sick, a person wore a surgical mask on my face during Ihraam.

Answer

If the person was really becoming sick, then although he had a valid reason for wearing the surgical mask in the state of Ihraam, he will still have to pay the kaffaarah penalty of having one sheep/goat slaughtered in the Haram, and all the meat must compulsorily be given to only the poor.