Can't really tell much from the sketches, but it looks like a diabetic version of an ammo sling (image attached below. Just picture insulin pens instead of shells).
I actually like your thought process as this is something that annoys me on a daily basis. At home, it's not a big deal and at work I use my briefcase. However, it's a pain in the a** when I have to carry around my bag of supplies.
Possibly helpful tip: if you could somehow find a way to customize a suit jacket to hold medical supplies discreetly, i think that would be awesome. That's currently the least annoying way for me as I can hide an insulin pen and meter in the various pockets without it affecting my night out.