I think going to the vet is the right thing to do now.
The cat havehas been sneezing for a week, so this is more than cats normally sneeze.
your catsYour cat's eyes lookslook irritated, and while this might be normal, it havehas lasted for some time, so you need to get it looked at by the vet.
The combination of sneezing and irritated eyes makes me think there might be an allergy or an infection going on.
So get on the phone and get an apointment atappointment with your vet and get this looked at.