According to the CDC itself, a NORMAL side effect of getting flu vaccines is feeling achy and having a fever. Check out these CDC links.
http://www.cdc.gov/FLU/protect/keyfacts.htm
http://www.cdc.gov/vaccines/pubs/vis/downloads/vis-flu.pdf
These normal side effects do not mean that it causes a person to contract an illness from it. (Think of side effects such as from medications. Some people get them and some don't). Also, having an egg allergy (and then receiving the flu shot) would most likely cause a more serious reaction.
Hope this helps!