Yes, sounds like an URI to me! That's how it started here at my house; Mr. B was sneezing non stop! A course of antibiotics, to prevent a secondary bacterial infection was prescribed and after a week, almost all his symptoms were gone. Of course, as soon as B got better, Oliver started sneezing!! It was like Kitty Kindergarten; one gets it, they all get it! I would take Sunny to the vet for a check and perhaps some medic. is advised!
They can be serious, but are easily treated. Oh, my kids are indoor only too! Get well hugs to Sunny from Mr. B, Oliver and Sandra