I have a dog and love animals, I don't have a problem with animals living in apartments. However, you have been keeping a pet when the terms of the lease specifically said no animals. The same thing happened to me a few years ago when I had tenants and they had a cat which they tried to conceal, I thought it was quite funny as I wouldn't have had a problem in them having it, it was a lovely cat. All they had to do was ask but they put themselves in the position of being in breach of the lease terms. When someone does something like that it tends to get people's backs up, so you have created the problem.
You can't make an application to the OC, you don't have standing because you're not an owner. The only way you could get permission is to ask the owner for permission and then the owner has to apply to the OC, so you need two stages of approval.
If you think the owner won't have a problem with animals (it is usually a standard term of a lease to exclude animals) then you could try that route, but otherwise perhaps you should monitor the situation and think about moving.