New to Backyard Chickens

[Ginger Dempsey]

I will tomorrow, I am sure he has roosted for the night.

Welcome to BYC. Yes, it does sound like your turkey might have a sinus infection.
Where do you live?
Is the swelling hard or soft?
Is this turkey a pet or food?
Is a vet an option?
Do you have antibiotics? Something like Baytril is what I would use if he's a pet (banned in poultry to be used for meat or eggs).

I live in Cataula Georgia, I haven't touched it to see . He is definitely a pet and although we have vets I do not know of any that take care of poultry. My husband gave him some Amoxycillin and it did not seem to help. I am going to upload a video.

 

[Ginger Dempsey]

This is my turkey that is experiencing allergies. I have ordered Vet RX which should be coming in on Thursday, but someone said it would not help.