What is wrong with my cat??

So I've never had pets. When my fiancé and I got our house we immediately went and got a cat...well ok..we went to get one and came home with two 😆

One of our cats is 1 year old and in perfect health. The other is 5-6 months old.

When we got them the younger one, Russ, had a runny, squeaky nose. They told us to wait a week and see if he gets better, if not take him to the vet.

He stayed the same. So we made an appt. They said it was just kennel cough and let it pass.

Well a week later, he was sneezing blood, still bad nose. But always playful and happy.

Took him back in. They gave him antibiotics. And now another week later. Still sick.

He has a crusty nose. You can hear him breathing across the house because its so squeaky. His eyes are also a little goopy.

Could it be allergies since the medicine didn't work?

Like I was prepared for the financial part of having a pet but I can't keep running to the vet if its pointless...