You really should take him to the vet and have him tested for a urinary tract infection. Spraying is a big sign of UTI. If it's not an infection the vet may give you something to give Felix to calm him. My cat Ripley was spraying and turns out he had a slight infection but he also had behavioral problems. He took antibiotics and Valium and it helped to get him to calm down and start using the litterbox consistently.

The stress of the new home, new dog and all these changes could have brought on his problems. Good luck.

Also, you might want to try something like Nature's Miracle to clean the pee spots well and then buy some Feliway to spray around to help calm him also.