Lots of advil and ice, the swelling is what's likely to be causing all that pain. And ditto the sling, that will relive some of the pressure. I don't think you need to go to urgent care, but if it's still hurting on, say, Monday, call your doctor. Don't lift anything heavy (like Cora) on that side for a few days if you can help it.
Rest, ibuprofen, and ice. I usually have lingering pain for anywhere from 48 hours to sometimes as much as two weeks (very light pain). It's possible you tore something, so I would say if it still hurts on Monday it might be worth getting in to see a doc. Unfortunately the only way they can really tell if there is a tear is by doing an MRI.
Oh man, I'm sorry swizz,. Ditto OPs, wear a sling for support, ice and heat, Advil for pain. Go easy - no carrying things for a while. If you go to the doc they'll give you an xray to confirm nothing is chipped or broken. It's probably unlikely but I'll leave that to your judgment.
Do you think you dislocated it or separated your shoulder? Only an MRI will confirm if the ligaments are damaged. You might want to follow up with an ortho doc after a month or so (it will take at least 4-6 weeks for the swelling to go down, they can't even see anything and probably won't manipulate your arm until after that point) at which point a physical exam may indicate if there's instability (meaning, you may have stretched or torn your labrum). Let me know if you need a recommendation.
I hope upon hope it was brief enough that you didn't do permanent damage.