elglocker, I have worked closely with doctors and used to own a billing center for anesthesiologists. While it's true that the hospital makes the rules, doctors often get a free pass or two as they are so hard to place - you and I both know this! It's not the same as an office job. The problem is you've now been given two free passes - you're running out of rope!
Now, since you've decided to carry, leaving the gun at home isn't an option, so you need to conceal very, very well. Having your actual phone near your gun is NOT a viable option, as you would have the possibility of showing your gun every time you grabbed for your phone. However, an old phone or pager that you can hang next to the gun gives you something to pull for show-and-tell if it's felt. And since you work in a hospital, you can also tell them it's a pain pump, insulin pump or spinal cord stimulator. If they ask to see it, just tell them you're a little embarrassed about it or in a hurry.
Finally, if your shirt accidentally "slipped up" over your gun, you are wearing clothing that is too short. Spring for the TALL sizes of scrubs, as they generally add 4" of material and don't allow that to happen even when doing somersaults. If the hospital won't supply them, buy your own - it's a write-off and worth it for your personal safety! For everyone else, many of the JC Penny's stores have a Big & Tall dept. in the store and carry Medium tall and Large tall polo shirts that do the same thing, as well as the XLT and XXLT for the larger guys.