oops
Fish: My mistake about the type of gun. When I think .357 Carbine, I think lever gun. I see, now, that you did mention in your first post that you are using a Ruger M77. My sloppy reading. Sorry.
Depending on where the sling swivel is mounted, using a sling may put sideways pressure on the barrel. Those fellows using ARs avoid this by installing a free float tube which isolates the barrel from the sling. if your carbine has a free floated barrel and you are attaching the sling to a swivel on the stock, you may be avoiding the problem. (I cannot tell from the picture of the gun at Ruger's website. Is the barrel free floated?) If, however, the barrel is attached to the stock at or near the swivel mount or the stock bears on the barrel at all, then there is a good chance that, once you sling up, get the butt onto your shoulder, slip your hand under the sling...pressure will bend the barrel/stock slightly toward your arm. It may not make a big difference for you. It is something to be aware of as a potential issue.
Do you have a shooting jacket?
Also, I have had a lot of success with Hornady's FTX .357 bullet at 140 grains
Pete