What is the best brand of medicine for pain related to inflamed sports injuries?

Anti-inflammatories. Ibuprofen or Aleve (naproxen) are the two most common but there are several others that work through the same pathways to help inflammation.
All NSAIDs work . Pretty well. Over the counter i tend toward aleve (naproxen) because you only have to take one pill two times a day with food versus advil that you have i take multiple times per day. Make sure you follow the directions warnings on the bottle when you take any med. Nsaids can cause bleeding, stomach upset.