Ask Mr. Smarty Plants

"Many instances of irritancy and possibly allergenicity resulting from contact with members of the family have been recorded.  The irritant (micro-traumatic) effects are attributable to minute needle-like crystals of calcium oxalate know as raphides, probably aggravated by steroidal saponins, proteases, and perhaps other constituents of the sap.  The allergens remain to be identified....Additionally, the thorny edges of the leaves as well as the needle-sharp leaf tips of many species are capable of nflictinig mechanical injury (macro-trauma)."

If one of the thorns of the leaf of the century plant broke off in your arm, you may have gotten some of the irritating sap inside the wound and there may even be a small piece of the thorn left within.  Whether or not you were exposed to the sap, puncture wounds of any kind are notorious for becoming infected. This is why it is important to remove the thorn as soon as possible and thoroughly clean the wound. Read what the Mayo Clinic has to say about puncture wounds.  It sounds like it would be a good idea to visit your Dr. to see why the bruise hasn't cleared up by now.