My right arm has progressively weakened since MS diagnosis 2002. I feel like im carrying dead weight around and wonder if I should use an arm sling?

Good question. This is a good question. There are times when an arm sling prevents injury to the shoulder, but it also gets in the way of using the arm. A better option would be to visit your friendly neighborhood PT and OT providers. They will have the best answer.
Complex. Yes, a support sling might prevent shoulder issues, but am more concerned about a secondary progression, and how this is being treated. Are you taking any potent MS agents? Are you supplementing Vitamin D-3? Have you tried PT, OT, Hand/arm therapies? Interventions can help, and perhaps a physiatrist can guide the way. Hope this will be helpful.
SEE YOUR NEUROLOGIST. I advice you should see your neurologist, meanwhile you may use a sling to support your arm.