Question

why does our skin swell and turn bluish-purple as a result of an injury

Answer 1

When the soft tissues of our body get hit sometimes the veins and capillaries lying just below the injured area break which causes leakage of Red Blood Cells .These Red Blood Cells get collected under our skin and this causes the injured area to turn bluish-black.These injured areas are known as bruises.The bruises first swell and look reddish and eventually they turn bluish-black.
Hope i helped u:) 

Answer 2

it is because of the nature of the skin called sclerodema which turns them into bluish colour