Perhaps the special function of a medical tricorder could be an autonomous Medic Hologram. It would be an extremely abbreviated version of an EMH, perhaps no personality, only enough medical knowledge to analyze injuries, determine priority for help, and have the ability to mitigate such injury until superior help can arrive. It could have the learning ability of the EMH, but it would take far longer to see any variation due to the smaller starting state, and the potential for growth would be far lower due to the storage limits of tricorders.
Due to any hologram being sizable storage wise, and requiring plenty of processing power, the types of scanning would be limited by having fewer scanning devices, and fewer preloaded scanning programs since most of them would not work without the associated sensors. Those devices and programs that are included would be specific to medical analysis in order to leave more room for memory/processing chips to run the MH. Medically, the medical tricorder (perhaps it should be medic tricorder) would nearly be the equal of the generic tricorder, but the generic tricorder would be a better analysis device in all other ways. As a result, the only people you would see carrying medic tricorders would be security personnel, soldiers, and perhaps civilians who expect themselves to be out of contact with civilization. Everyone else would use full function generic tricorders, especially when in contact with a network capable of running an EMH for the tricorder.