Is it possible to spread the flu from getting a vaccine?

I recently received an H1N1 Swine Flu vaccine shot, and started having mild symptoms such as fever and congestion. However I am not coughing or sneezing or anything like that. Can someone who accidentally drank from my cup now catch swine flu? I understand that the Shot form of the vaccine does not carry the live virus, so it shouldn't be able to spread. Am I correct?