Based on your symptoms it seems that you might have injured your shoulder muscle or its tendon. The correct way is to go and see a physical therapist with an experience in sports related related injuries for an evaluation and treatment.
Next Steps
Start with pain medication and anti-inflammatory to reduce pain and inflammation in soft tissue, rest and ice. Say no to right upper extremity workout for at least 3-4 weeks, it could take 4-6 weks to heal.
Health Tips
Rest and apply cold packs 5-6 times a day for 15 min duration.