Can cats get seasonal allergies?

Ok, first off, in answer specifically to your question, "yes", they can get allergies. However, you NEED to take her into the vet. Those symptoms can be for a variety of things that I JUST discovered for my cat, which turned into a very long ordeal. It can be an Upper Respiratory Infection, the allergies can turn into asthma/allergic-bronchitis, or some kinds of infectious diseases. I don't mean this to scare you, only to warn against uming that symptoms for cats work like ours. I really really recommend taking to the vet! Hope she gets better soon!