Most people take Aleve or ibuprofen after an injuyr only when they're hurting the most. It's very often that we hear "I take as little medicine as possible." Thats great, but to get the most out of these medicines after an injury, it's important to take them on a scheduled basis, even if you feel like you don't need it right then.
These medications are anti-inflammatories, so they are not just masking the symptoms, they are decreasing the swelling and inflammation that is the source of your pain. As the swelling and inflmmmation go down, so will your pain. And as always, make sure you're dosing any medicne as directed by your doctor.