Trumpets aren't heavy enough to give you the kind of left shoulder pain you get from wearing a heavy electric guitar on a strap for hours. It's not the weight, IMO, it's the grip. Tension in your grip holding the trumpet sends tension up your arm (where else is it going to go?). That's basic. Get a grip.
Get a lighter grip. Switch to an Olds Recording and enjoy holding your trumpet without any of the TENSION you need to keep on that 3rd slide ring to keep it closed. No tension necessary .... you only apply a little when you want to work the slide. It may not seem like a lot of tension to keep the slide closed, but over time, you may be surprised, or end up with a sore shoulder. Try lipping everything for a while, quit using the slide (clamp or tape it shut) and let go of the ring. See if that eases up the left hand grip. You can hold it as lightly as you want, especially if your right thumb is where mine is ....... in between the 1st and 2nd valve, under the leadpipe. The right thumb in this place can take a lot of the weight off the left hand, so that, with the trigger, I can just lightly cradle it with the left.