Your 124Gr RN might work OK for 38Special, but it you're shooting it in a revolver, make sure it has a crimping groove to prevent the bullet from walking out and binding.
I find that this profile works well for my 9mm and a 38Super.
http://www.missouribullet.com/detail...ry=9&keywords=
In both cases, I use them sized to .357dia. Can't imagine why it wouldn't be fine for 38Special as well.