I had heard that people getting the injection, sometime get sick afterwards.
Yes, some do. Some folks getting the flu shot also break bones afterwards. Correlation does not imply causation. Given the Vice President's age and medical history, I'd venture to say that he is better off receiving the flu shot than not.
I'm glad to hear that our VP is well. May he continue to cause DUers to weep in their bong water for another four years.