I'm so sorry to hear this!
As others here have said, maybe the best idea is to have a talk with your landlord and with the neighbor. Explain the situation and promise to never let it happen again. After all, if there has never been a complaint against you before, they should really take your word for it.

I really hope you don't have to give them up!
We've got our paws crossed for you!

Love,
Thelma, Elvis, JD, Yertle and TimTam.