I am really sorry for all you and cooper have to go through. Buffy my golden mix who is a rescue, when we got her and she had been hit by car, she had to be on steroids for a long time, and did the same, she peed herself, we put out puppy pads all over the floor, that kept her from getting soaked when peeing, but you could tell how badly she felt when she saw us lifting her up with the towels under her belly and changing, she knew she had peed and hated it.
I hope you dont have to deal with another surg. But think positive, even if there should be a damaged urethra, I know they have drugs (not saying that is going to be a sure thing for him, but dont think surg. straight away) the drugs are known as alpha agonists, and they stimulate the neuromuscular receptors of the urethral muscles. But it is not uncommon with temp. incont. after surg. But since he seems not to be able to go, it sounds like a uti and that can be sooooo painful, I cant believe that the vet. didnt want to do a test on him to make sure that is not what it is, that is rather easy to fix and would help you and him so much right now.
Be strong, you are doing great and when you want to tear you hair off, go sit with him and look at that sweet face and youll realize it is all worth it. Let us know how things go and I will be thinking of you and send some good pee thoughts your way.
huggs
Marit