Can you hit a blood vessel on your elbow by hitting it on something?

Yes. If you bang your elbow hard enough you will end up with a swollen elbow that becomes bruised (black and blue). The swelling is from the tissue trauma and the black and blue is from bleeding under the skin from usually a ruptured vein. Over several days the blood from the vein rises to the surface and is seen under the skin only then to resolve over several days.
Not. Blood vessels are well protected in the elbow. The ulnar nerve can be felt but no blood vessels.

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