Lie to him (or maybe it isn't a lie and I just jynxed it) and suggest the consequences of not going, for all you know, maybe it could be a sort of infection that could permanently damage his sex glands and he won't be able to have kids anymore.
Who knows? He is being childish for not going, it sounds serious.
Do these thick white chunks have a particularly foul odor? Do they come out of the penis hole or is it being produced on his head under the foreskin?
If it smells terrible and it forms under the skin, I would assume that it is the production of smegma. It's like a natural soap remnant when the penis tried to get rid of something irritating it. But that would imply that something he is excreting is causing the irritation.
However, I have a good feeling this isn't the case, and it isn't just smegma due to some irritation. I wouldn't call smegma thick, nor a chunk.
My second hypothesis was that he may have kidney stones or something of the sort. That would explain the abdominal/bladder pain, and the white substance would be calcium oxalate deposits forming. But again, this is a weak hypothesis, I don't know if the penis can excrete large chunks of calcium like that. But if you want to give it a try, just in case, keep him off foods with calcium.
I am basing this only on logical deduction, not as a professional who has thoroughly researched these related fields.
I really do suggest you knock him over the head and take him to the doctor. You don't want him to end up with permanent damage. I'm sure he wouldn't want to regret feeling stupid afterwards with permanent urinary/penis issues for "trying to be a man" and not going to the doctors.
Keep us updated and let us know the results when possible so that we may be able to aid others in the future who may have this problem