I assume you had your blood drawn from the bend in the elbow, known as the antecubital space.
The biceps tendon inserts into the forearm bone, the radius. On occasion, the needle can pass thru the front of the vein and then the back of the vein. During the period where the tourniquet is on, when the needle is pulled back (since you cannot get blood when the tip of the needle is thru the vein), then the hole in the back wall of the vein will bleed, but the blood will be contained in the space where the biceps tendon is. Afterwards, this causes pain and swelling. Over the next few days, like any bruise, the blood will break down, causing discoloration around the elbow area. Heating pads applied to the area will speed up the reabsorption of blood.