My 3 yrs 11 months child was injected flu vaccine last sep.22 but now have colds since yesterday same goes with my 8 yr old nephew. Why is that?

INFLUENZA. Flu vaccine protects from getting influenza including swine flu, which is one of the worst viral illnesses. There are lot of other viruses/winter viruses which flu vaccine doesn't protect. Your child, his cousin probably gotten one of the cold viruses. During weather change time, kids get cold symptoms. Treatment is supportive, make sure they drink enough fluid. If any worsening, talk to the doc.