I'm kind of curious why you posted this in "Online Auctions"?
But anyway, I would definitely let the supervisor know, just so that if anything happens - like your blood sugar crashes, then they will know what is going on.
Just let her (him?) know that you really don't want it to be public knowledge, because it tends to single you out. If you are straightforward with them, then they figure you aren't asking for preferential treatment.
Congrats on the new job!