You need two YN-622C triggers; the YN-568EXII does not have a radio receiver built into it. It does have an optical sensor and can be used as both a Canon optical master or slave; as well as a "dumb" optical slave with any flash burst setting it off.
However, Canon only put a master into the pop-up flash of the dRebel line with the 600D and later models, so to use this system, you'd need another master unit on the camera hotshoe (e.g., a 90EX, ST-E2, 580EXII or 600-EX-RT) if you wanted to use the flash wirelessly with TTL function, which is likely to cost more than a pair of YN-622C triggers.
The YN-568EXII also has the S1/S2 "dumb" optical slave modes that can be used with the 550D's pop-up flash (or any flash for that matter) set to Manual (S1) or eTTL (S2).