Planes can be germy places, in addition to the air being recycled through the aircraft, there are things that are used on every flight that is only cleaned once a day or maybe not at all.
According to a former airline attendant, blankets aren’t swapped out or cleaned in between flights, so yes that person who was sneezing all flight probably did so in the blanket that you’re covering up with.
One Reddit user revealed that “Only fresh ones I ever saw were on an originating first flight in the morning in a provisioning city. Also, if you have ever spread your peanuts on your tray and eaten, or really just touched your tray at all, you have more than likely ingested baby poo. I saw more dirty diapers laid out on those trays than food. And those trays, yeah, never saw them cleaned or sanitized once.”
According to those that fly the friendly skies the most, blankets are usually just folded up and a clean one is only available at the beginning of the day, same for the food tray which is only cleaned overnight.