Hi Breonna,
How old are they and for how long have they been coughing and sneezing?. I am not able to help much with your problem but this additional information may help the person that is knowledgeable enough to answer. I hope they are better soon!
Diedra
Hello,
Spaying might help. Big emphasis on might. I would say this is going to take time and boundaries. There is no other way around it. It is very common for the family dynamics to change with the addition of a new pet. You can try to isolate and spend time independently with everyone. Or try caging the aggressor intermittently to see if that helps de intensify the situation (but better wanted it might make the stress worse). Or find a separate place for your ferret and get him his own friend. Really my biggest concern is the ferrets safety. It will take time to see if they can work it out. But I don’t want to risk him in the process. Whatever the resolution might be I encourage you to stay optimistic. Try not to make matters worse with stress or reprimand (Never ever works on animals!) and just trying lots of options. Like adjusting feeding placement and attention rewards for the food behavior.
Ask your vet for help from a behaviorist. And get the cat spayed. If needed ask the vet about behavior modification assistance. There are lots of options there. Very best of luck!