The lowdown on insect bites

Yesterday I got bitten twice in the legs by this insect with a green body and legs about 1cm long. I have been bitten by insects a few times before but I have never reacted so badly to this. The places where I was bitten have swollen up to reach the size of my palm or has swollen the side of my right calf.

Can someone tell me the in’s and out’s of how exactly this happens? What does the swelling consist of? Why is the area of swelling so large for a bite so small that I can’t even see it? I heard something about the insect giving an enzyme which stops the blood from clotting…