I got my flu shot five days ago and the area is still red, swollen, and tender and getting larger. is this something to be concerned about?

Concern, yes: This is not the reaction we want. Can it happen - it can. I would advise you to try hot warm compresses without burning yourself. (some may like ice, but in this case i would try heat). If you don't start to see slow improvement, you need to inform the doc who gave you the injection. You may be developing a reaction to the medication, or an infection.