I'm confused as to the timeline here. You mention in your summary that it's in the present that Roxas only has 6 months to live, yet the only mention of this is in a flashback that has no real time anchor, leaving me confused over whether this is a recent happening or something that happened before his surgery. This is doubled up by his lack of apparent urgency upon finding his previous donor, which seems to be more a case of 'I just want to find this guy' rather than the 'I want to find this guy cause he might be able to save my life' that you mentioned in your summary.

Also, the only reason why I can think of a doctor ever not offering medication to a sick patient is in the case that the medicine will have no effect or be detrimental. Unless you really want this doctor to be memorable as a giant arsehole, I don't see why he can't at least give Roxas some painkillers or anti-nausea pills.

Aside from this, I like your writing, and I'm interested in seeing how this will play out.