I got bloodwork done 4 days ago and ever since ive had a blue bruise on my inner elbow where the blood was taken. is this normal?

Perfectly normal!: When blood is drawn, the vein is pierced by needle and so leaks blood, causing a bruise. Sometimes the bruise is bigger than at other times, but it should go away in 7 days like any other bruise. If you should notice increased pain, warmth or red streaks, then get checked right away for a possible infection (though this is rare after a blood draw, if you keep the site clean and protected.

Blue bruise: The blue bruise is called a hematoma which is caused by of obtaining blood from your vein