Gunshot wound to the arm - aftermath?

I would start the story a few months or so down the line unless his rehabilitation is part of the story. My then, his major damage should be minimized and he would more than likely just do self rehabilitation exercises or treatments.

A 45 is pretty big slug and does a lot of damage. If no bones were hit, the muscle damage can be repaired, it just takes a lot of time, depending on the victims previous health. Repairing the Artery is the easy part, and nerves in muscles will reroute or regenerate as well, just along new path ways....

Muscles in the arms and legs can regenerate and they are experimenting with heart patients, by taking samples of their own muscles, growing new muscle cells, and then injecting them directly into the heart to repair damaged hearts, since the heart is ... a muscle.

You can get away with quite a lot in terms of how well he recovers, but the general assumption would be serious muscle damage, decreased range of motion, and likely nerve damage to boot. Just realize that you're punching a half-inch hole into his arm (you can look at your own to see what you'd clip if you did that), and--assuming it's a penetrating rather than grazing shot--a larger hole coming out. That's going to tear muscles (or put holes in them) which generally requires surgery to heal properly, remove large patches of flesh, and cause a lot of shockwave trauma in what's called a temporary wound cavity.

I wouldn't plan on him using it any time soon.

I've butchered a LOT of deer over the years. The meat (muscle) surrounding entry and exit wounds is not usable except as cat food (if there are no metal fragments). Entry wounds aren't as bad, but everything around the exit wound (for several inches) turns to mush, like it's been pureed.

If the slug expanded upon exit, he could have a 2 in or better exit hole surrounded by macerated muscles, tendons, ligaments...there would be substanial tissue loss (like the deer). With damage to the brachial artery, he would also have damage to the median nerve, which would be generally bad news. You definitely want to research that, because the severity of the nerve damge impacts functionality of the arm and hand. He would probably regain the use of that arm eventually, but nowhere near 100%. In this scenario, he'd be on the DL for 6 months to a year.

If the slug goes straight through, the tissue damage isn't so bad, but you still have to address damage to the median nerve.

there is also a risk of sepsis due to the junk brought in with the cavitation wave... where exactly is the shot?...it would be real deforming...

In response to cornetto, the hydrostaic damage from a .45 is minimal compared to a rifle. Although if you were talking about deer taken by a handgun, I apologize in advance.

A broken bone would be a nice change to all these flesh wounds protagonists always walk away from.