Time for Neurologist. These are such unusual symptoms that have followed allergy shots, so one should be cautious about blaming the injections on these new problems. Any injury to the body may cause a condition known as reflex sympathetic dystrophy/crps complex regional pain syndrome, but it is hard to imagine that allergy shots could bring on such a complication. Please arrange to see a neurologist now for workup.
Ask your allergist. Your allergist needs to know about this and any other reaction you may have. Depending on your immunotherapy prescription, pain can come from having too high a glycerin content in your vials, and may go away if they are made more dilute. Unless you've had a mastectomy or other procedure that affects lymph drainage from the right arm, you should alternate arms between injections.