Shaking- adverse reactions to the seasonal flu vaccine are rare, so if that is what you have, then no, it is not a normal reaction.
One cautionary note - We often confuse correlation with causation, so it is possible that you were incubating a cold which has chosen to manifest at around the time you had your shot.
The more common adverse reactions to the flu shot tend to be localised, transient and mild - so soreness, redness or swelling around the injection site.
Rarely, more systemic reactions are observed - again these tend to be transient and relatively mild - most common are low grade fever or malaise - a sort of generalised feeling of unwellness.
All symptoms should subside within 1-2 days max.
If you have any concerns over your response to the vaccine, you should contact NHS direct in the first instance ;
http://www.nhsdirect.nhs.uk/