Hi think it would be great idea to have cultured the germ that caused the pus since certainly, was a slow growing organism. However, pus around the elbow could easily attain the elbow joint. Doing an A ray of the elbow to ensure the integrity of this joint could be a good idea.
Consult your primary care
physician for a better follow and search for the cause or predisposing factors to this scenario.
Just the best,