To put my two cents in on the issue of an inmate being a part of the medical staff or even helping out, it seems highly unlikely. Too much small contraband--drugs, things that could be used as weapons or easy made into weapons--would be available in the hospital to allow anyone uninjured access to it, and prison hospitals generally aren't reknowned for taken good physical care of inmates, to say nothing of their mental health. In prisons people are more likely to receive psychiatric meds, but I know a person with schizophrenia who was locked up in jail for several months without any medicine for his illness. Other jobs, such as working in the cafeteria, or doing menial labor, inmates are afforded a chance to do, but always supervised, and always with a careful accounting of anything they make use of. If anything goes missing, even the smallest bit of metal, they would immediately lock down the prison and run a thorough sweep of every inmates' cell, even if they were not present when the item went missing, in the event they passed the contraband on to someone else for safekeeping. Inmates may also be searched, who knows whether they would do body cavity searches in such an instance.
I am curious about what form solitary takes in the prison. Sensory deprivation--as in no light, no sound, no human contact--are pretty common, and sometimes the places where someone is kept are very small, forcing them into an uncomfortable position for long periods.
I was also wondering if you had put any thought into whether or not the prison includes a common area, and a recreation area, or whether or not inmates are allowed outdoors. If so, how long might they be allowed to be there in a 24 hour period? Such an institution would be highly regimented, everything going on a set schedule every day, no stops no breaks. Food for thought I guess. 
It goes without saying that there are some facilities that maintain a twenty-three hour a day lockdown, with one hour allotted for recreation outdoors, the rest of the inmates' time being spent in a cell. That is an extreme example, of course, ad one which severely limits chances for interactions between characters.