Although we see it precious little (regeneration sickness, hand getting cut off), one kind of has to assume that over his hundreds of years, the Doctor gets sick or injured from time to time. So how does he make it through? Who doctors the Doctor?
During One’s era, we occasionally saw the TARDIS crew take advantage of the First Aid kit, though Vicki didn’t necessarily trust its contents not to be barbaric, given the time from which her crewmates originated. There was also the Zero Room when Five was having a rough time of his regeneration, and that “device” Three had Sarah Jane retrieve when he was ill on Metebelis III well before the incident that caused his own regeneration. Other than that, though, we haven’t really seen much in the way of medical facilities on the TARDIS. Does she have a sick bay? Even if she did, who would be qualified to treat the Doctor there?
I suppose there are several options. Either (a) the Doctor is immune to most diseases and injuries, (b) he is incredibly lucky, (c) he is able to heal himself off-screen with facilities or abilities never introduced to the audience, (d) he carefully selects a facility he trusts somewhere in time and space and has the TARDIS take him there, or (e) he uses that healing with regeneration energy crap he pulled recently to heal River.