Vomiting blood, is not any seasickness I've heard of. Maybe ulcer, perforated something, but not seasickness. My crew was vomiting blood, especially bright red, I'd get him to med services ASAP.
Again, I would ask why the person refused medical treatment once ashore. That is what piqued my curiosity along with saying they were taking on water rather then sinking. Could be bad reporting I don't know but it does makes me wonder.