Hey, cool, nice to meet someone mostly in the same boat. My right foot is also totally flat and my left foot is arched too, although it sounds like maybe your left foot is more arched than mine if you developed a stress fracture on that side. My solution when I developed an extremely painful right knee was to get custom orthotics (both feet). What did your podiatrist prescribe for you, anything besides a stability shoe? That or a motion-control shoe is appropriate for most overpronating flat feet, but a more highly-arched foot needs more cushioning, not more rigidity.
Be careful in adjusting just one side, because you don't want to make your left leg functionally longer by adding arch supprt to that side only. If your right foot is what's known as flexibly flat, meaning it looks like it has an arch at rest which disappears flat when you stand and put weight on it, both of your orhotics will conform to each arch at rest, because that's how each is individually casted. Then, with the appropriate support or cant under each foot in the form of a custom orthotic, you can probably get a pair of more neutral shoes, since each orthotic adjusts each foot as needed.
I've always heard exercises won't make much difference in building up our flat right arch (and I did give it my full effort when my right foot became flat), but I've seen a lot of runners' blogs lately where they claim to have built up their arch(es) by using Vibram Five Fingers or even running barefoot. Any flatfoot runners here with that experiece? It sounds too good to be true, but I'd be willing to give it a try if there's proof of this, like before and after photos of an arch where none existed before, or even a low arch turning into a visibly higher, strong arch?