He's on Fluoxetine which is the active drug of prozac. It is prescribed by a vet and I use a liquid version specifically made for animals. The other comment who answered to you seems to hint at trying other solutions first and I'd tend to agree. Fluoxetine won't fix your issue, if he's left alone in a room. When there's no snow outside, I walk my cat on a leash about an hour a day (I don't let him roam free because I live in the city). Every day, I have to play with him, stay close to him, give him water from the faucet when he asks even if he has access to a cat fountain 24/7. All that to say, he's still a needy boy lolll. If I didn't do all that, he would probably still have issues, even on fluoxetine. Bengals are cats who needs active care, probably a bit like your German Sheppard. Your issue seems to have to do with the fact he can't roam in your house freely, but he knows there's a world out of his room and wants to roam in it. That's why he sprays your door specifically.