Keep up the good work. Couple years ago I took an abandoned twin bull calf from one of our neighbors to foster on our milk cow, since the neighbor didn't want to bottle feed, and he got really sick a day or two after he got here. He was only two or three days old, poor little guy. The neighbor said he wasn't sure if he got colostrum or not, and totally expected him to die, but I did what I could for him and he pulled through.
All I had was penicillin, so he got that every day for about two weeks, and was kept inside the barn except on sunny afternoons. He got all the milk he could drink from the cow, and eventually he shook off the crud he had, but man, it took a long time. A month, at least. I would have given him something better than penicillin, but he wasn't my calf, and the owner didn't want to spend money on expensive drugs for a calf he was convinced would die. So he got what I had, because frankly, I didn't want to spend $400 on a calf that wasn't mine.
Anyway, after all the penicillin, I gave him lots of probiotics, and Vitamin ADE paste, to help him along. Sometimes, especially at the beginning, I could hear his rattly breathing even before I got to the barn. But he slowly got better, and went back home several months later, healthy and frisky. He sometimes coughed after a run, so I'm sure he had some permanent (or at least long-lasting) damage to his lungs, but other than that slight cough after exertion, you'd never know he'd been sick. His owner was amazed he made it, but it was just because I had the time to spend tending to him, and I hate to see babies die, so I tried as hard as I could.
It was ironic that I spent so much time and effort to make him well so he could be beefed, but it was another lesson in the Veterinary School of Hard Knocks for me, so it wasn't a wasted effort. I got some experience, and the neighbor got to send the calf for beef eventually.
As long as your calf is perky and finishing his bottle, he's got a good chance. Hopefully he'll make a full recovery, too.
I also hope I'm not speaking out of turn here, because I'm NOT a "cattleman" like most of you, but I did have that one really sick calf, and this one sounds very similar, so I thought I'd post this as encouragement.