Raised warm rash spreading, flu shot? Cellulitis?

My aunt is 84 and has a very bothersome rash on the back of her upper right arm.  She got a flu shot on Oct. 31. On Nov. 9, she developed a red blotch approximately the size of a baseball that was very itchy, warm and sore.  Her doctor initially thought it was a reaction to the flu shot.  Shortly thereafter, the rash spread to her back and side, part of her left arm, as well as her ear (all with the same symptoms- red, itchy, hot).  Her doctor prescribed Keflex (500mg) in case of cellulitis, which did not cure the problem.  Today, her doctor claimed he did not know what the problem is and prescribed a steroid as well as an anti-itch pill.  She works as a volunteer in a hospital gift shop, and also takes a low dose antibiotic regularly for chronic uti's.  My question is, could the rash be caused by a resistant strain of bacteria that the Keflex would not have killed?    

[grant1966]

Was the rash cured by the steroid? My husband got the H1N1 shot and 9 days later developed a skin rash - also red, blotchy, warm and sore. The doctor told him to take Reactin, which has done nothing to help the rash. The rash has in fact spread. It is not an allergic reaction to food or soaps - nothing new has been introduced into his diet.