Paint looks like its flaking off rear bumper
That's because it is!
I suspect the paint was already starting to lose its adhesion before your wee mishap. It might also be worth taking a close look at the other bumper to see if there's any sign of the paint delaminating from that one. I see this quite often on cars >7yrs old, and not just Fiat's either.
Bumper off the car, strengthen any cracked areas from the back, fill the front as necessary, sand down completely, then prime and respray the whole bumper.
You're not going to be able to successfully spot repair this.
If you have another vehicle to transport it, removing the bumper and taking it to a professional bodyshop might be worth considering.
I'm guessing somewhere in the region of £250-£400.
But it's a plastic bumper, won't rust, and the damage is purely cosmetic, so just doing nothing is also an option.
