There are two issues here:
1) The nature of security at the hospital.
2) Whether certain patients should be allowed to retain their firearms on hospital premises.
I have some experience of both of these from the point of view of a health worker and also a patient.
Firstly I agree that it is likely that security at the hospital is going to be fairly 'nuts and bolts' if you know what I mean, unless there are dignitaries being treated there. I've seen some hairy situations in South Africa in a large trauma unit where the security guards were only armed with batons and there was a no firearms sign and a policy of no staff members carrying firearms whilst at work.
This latter policy was not as rigorously enforced by security because the majority of 'carriers' were doctors who were stationed in the casualty department very close to where the security office was and there was (unofficially) some comfort in that fact for the security guards. Many of these doctors were also reserve policemen.
If something bad happened in the casualty department (armed rival faction or irate customers) then the procedure was to call the Flying Squad, who would often get there pretty darned fast. In the meantime there was the (unofficial) presence of armed health workers.
You have to understand that the health institution is a warm, fluffy, caring thing that doesn't want to distress patients and visitors with the presence of side arms on the hips of the minimally-paid security guards
The potential for litigation in the event that a patient or visitor is exposed to all the horrendously negative and psychologically devastating effects of a firearm discharge is significant...and compounded by the potential 'bonus' prizes of projectiles being in the vicinity of sensitive 'stuff' such as hazardous gas containers, electromagnetic radiation equipment etc. As much as I am trying to breathe a tone of hand-wringing and arched eyebrows into this description, there will be some bean-counter or advisor to the management who will have convinced them of the relevant risks a lot more eloquently than I can.
In short, armed guards are going to be in the minority (if at all present) at most hospitals.
Okay, what about a patient who is armed?
Well a patient isn't just a patient. He could be Mr Jones coming in for an annual chest X-ray and clinic visit for cancer surveillance. It is well within the bounds of reality that his firearm hasn't been seen by security and he arrives in the X-ray department or the clinic with it in an IWB holster or a man-purse.
When I see that guy, I don't call security to tell them to get this guy's gun and check it in. It's a judgment call: the guy isn't going to be admitted, he isn't an obvious threat to himself or anybody else, his demeanour doesn't make me worried about him because he is armed. His clinical history doesn't give cause for concern. He isn't going to be admitted, he will be on his way home in a few hours. See what I mean?
The next one could be drunk, irritable, or otherwise 'not up to par' with the standards you would impose on a stranger who was in contact with a vulnerable member of your family (such as a child) whilst being armed. To word it another way, you wouldn't feel comfortable in their presence if the two of you and a third party who didn't know anything about firearms were sitting in a bingo hall or manning the same stall at a homebake sale. You either want him done and dusted as quickly as possible or there is nothing for it but for him to be disarmed whilst he undergoes his treatments. How that happens is the subject of a different debate.
The OP is somewhere in between (for the sake of argument). He isn't in the best of nic and has an undisclosed firearm. This means that no provision is afforded him, for the secure storage of that firearm during his stay.
And that's the part that I think is an issue. He may not believe himself to be a problem, but there are treatments that do impair your ability to reason and there are side effects from sedatives that make a person incompatible with the safe handling of a firearm.
An example for the OP is a bronchoscopy. He doesn't specify his medical history in detail, but it is entirely within the realms of reality that he can undergo a planned or emergency procedure that makes him unfit thereafter to handle a firearm.
What about other patients? Is this a general ward, or a locked private cubicle that only the OP occupies? My experience is that all-and-sundry have access to wards and cubicles and that a patient cannot even trust staff with valuables these days, never mind a light-fingered fellow patient. Who carries the can if someone takes that 1911 while the OP is downstairs having a CT scan of his chest?
There are very few scenarios where I can think of a legitimate reason to allow an inpatient to keep a firearm in the manner that the OP has stated. Doesn't mean I think the OP was dangerous, it means that there are variables and circumstances that he hasn't thought of that could land him and the hospital administration in a jumbo-sized pile of excrement should things go awry.
And I'll tell you something for free...in hospitals things DO go awry, make no mistake!