Zyrtec can cause a host of issues (i.e., irritability,anger, depression, hyperactivity) with children to the extent that many parents have taken them off of it. I (an adult....) was on it recently for the first time and definitely noticed irritability,anger & depression issues with myself. I stopped the zyrtec and am feeling back to normal.
All antihistimines can sometimes make children more "hyper" b/c they sometimes have the opposite effect on children than adults. (Zyrtec makes many adults drowsy). The nosespray shouldn't have any systemic effects.
But if your child isn't irritable or anxious, I would wonder if maybe he isn't so much hyper as he is finally feeling much better and has more energy. Allergies can really take a toll and make you very tired and lethargic.