Finish the Ivermectin if that is what you are giving him, I think you said you had one more day ???
@Southern by choice says that they successfully treated lung worm with ivermectin and she is one that I trust.
Do you live in an area where it even could be lung worm? Was the kid living on a wet pasture where there is standing water? Are you in an area where lung worm are prevalent?
The vet wanted him to take an antibiotic...did he say why?
Did you have a fecal done on him when you took him in? If not, I would collect some goat berries and get one done but since he is on medicated feed probably not cocci but it never hurts and it should be relatively cheap.
Sometimes goat get a respiratory ailment when they are weaned and when they are transported...stress related really. I don't have lung worm where I live but I do have goats that cough; they go on an antibiotic if it doesn't clear up in about a week.