A large scientific review of a number of studies found that no one NSAID appears more effective than others. Interestingly, they also found that using NSAIDs was no more effective than non-pharmacologic interventions (spinal manipulation, physical therapy, bed rest) when it comes to the treatment of headaches. In general, the same can be said for shoulder injury.
If conservative measures do not produce desired pain relief and functional restoration (getting your range of motion back!), NSAIDs and Acetaminophen are the recommended first medication choice for treatment for both acute sprain/strain and flare-ups of chronic sprain/strains of the shoulder. They were both found to be similar in helping in the recovery of acute pain. But watch out for the stomach and liver side-effects.[i], [ii], [iii], [iv], [v], [vi]
[i] Lanas A, Perez-Aisa MA, Feu F, Ponce J, Saperas E, Santolaria S wt al. A nationwide study of mortality associated with hospital admission due to severe gastrointestinal events and those associated with nonsteroidal antiinflammatory drug use. Am J Gastroenterol. 2005 Aug;100(8):1685-93
[iii] Fine M. Quantifying the impact of NSAID-associated adverse events. The American Journal of Managed Care [01 Nov 2013, 19(14 Suppl):s267-72
[iv] Chou, R. Pharmacological management of low back pain. Drugs. 2010 Mar 5;70(4):387-402.
[v] Wolfe MM, Lichtenstein DR, Singh G. Gastrointestinal toxicity of non-steroidal anti-inflammatory drugs. N Engl J Med. 2007;147(7):478-491.
[vi] Hawk C. The Praeger Handbook of Chiropractic Health Care.Santa Barabara CA: ABC-CLIO; 2017.