Flu vaccinations protect against flu. They will not protect you against the many other viruses that are around every winter. Some of these cause similar symptoms to flu, and are often called 'flu'. But flu is generally more serious than these other infections, so it still makes sense to have a flu vaccination. The vaccine does not contain any live virus, so it cannot cause flu.
Flu vaccinations are very safe.
You may get some soreness where the vaccine was injected. Less often, people get a slight temperature and aching muscles for a couple of days after being vaccinated. Other reactions are very rare indeed. You should not be vaccinated if you have a serious allergy to hens' eggs. Vaccination is generally not advised if you are pregnant.