I was finally able to find some ammo for my new to me Smith and Wesson 629 6 inch. Firing of one round is unpleasant, the second round is borderline painful, and the third round simply hurts. No more, thank you.
Am I a weakling, is this normal, or is Callahan a monster?
OP, you are not a weakling. Here's the thing...for me a big part of target shooting is the fun aspect. And part of that ties into the satisfaction of hitting targets. And doing so without enduring a lot of discomfort and / or pain.
A few weeks ago, a fellow range member kindly brought his 686 in .357 Mag for me to shoot. I have never shot a revolver before and bought my own .38 Special to try out. The recoil on the .38 special was fine...then he brought some .357 Mag for me to try.
It was a significant difference; not just in my hands, but also in my wrist. Now, I am a small middle aged guy. Don't exactly have John Cena physique. And I recognize my limitations. Can I get used to .357? Probably - over time...a long, long time. Would I want to shoot anything stronger than that? Probably not at this point. Does that make me a weakling? Don't care. I don't have anything to prove, don't need to play a game of machismo with anyone and to circle back to my original point, I want shooting to be fun. Just like any other activity, once it ceases to be enjoyable, both the interest and time invested will wane.
I am not getting any younger and my family has a history of arthritis. I would love to continue shooting into senior citizen-hood, and part of that is recognizing and being comfortable with my physical limitations and tolerances.
That said, it could also be the gun and the mating of the ammo. Many years ago a friend let me shoot his Browning 12ga pump action. At the time I had an 870 20ga shooting 7.5 to 8 birdshot only. Little did I realize he loaded his 12ga with 3 1/2" magnum rounds. After the first shot, my shoulder ached for a while and I swore off any 12ga shotgun until last year when I bought one and some low recoil 12ga slug. Years later, shooting 12ga ha become more manageable, but that's also considering the difference in the gun, ammo and much more trigger time with various calibers over the years. I am sure one day my body may not be able to enjoy 12ga anymore and if that happens, I'll just drop down to the 20ga again or even 410 or whatever. No harm, no foul. As the saying goes, you do you, I do me.
So I'd say if you don't enjoy 44 mag, maybe drop down to 44 Special, or as others have said perhaps a reloading recipe may help reduce the power. Or consider a different gun and ammo mating to experiment.