I hit my elbow really hard...should I be concerned?

So yesterday early evening I was taking down the big umbrellas on the veranda at work. They are really top heavy, so my usual method of folding them down is pulling the key out and ducking really fast to avoid being whacked in the face. In the midst of doing this, I rammed my elbow on the top side of a chair, right at that soft spot between the bones. I guess this is what they call your funny bone? It hurt SO much I got really dizzy and was laughing and crying at the same time. Afterwards, and since then, I have numbness in my forearm and hand when my arm was relaxed or extended, and when it is bent or I am pushing, pulling, or twisting something (like a mop or door knob), it hurts so much that my whole body trembles from trying to control and endure the pain. The elbow itself has a nice ugly blue and purple bruise where I initially hit it, and then right next to it is a bit puffy and tender, and sort of pinkish in color. I've been taking advil to sort of dull the pain, put ice on the spot to reduce swelling, rubbed icy-hot to relieve the internal pain...and it's not doing much. Sometimes, especially at work, when I have to carry something heavy or use my arm in a motion where I have to just bite my lip and endure the pain, afterwards I feel really tired and a little dizzy. Just typing this question has been a struggle. If it's nothing to be completely concerned about, or if there are better self-healing methods I can try, please let me know. I would rather NOT waste the 150$ to see a doctor for 15 minutes for him to tell me I'm fine.