I hit an area of my elbow and had a burning sensation throughout my hand

It's often referred to as hitting your funny bone:

Heres one reference on the subject: https://www.huffpost.com/entry/hitting-your-funny-bone-i_b_12201698

and here is another: https://www.mentalfloss.com/article/21474/what-funny-bone-and-why-does-hitting-it-hurt-so-much#:~:text=When%20you%20hit%20your%20funny,the%20ring%20and%20pinky%20fingers.

The ulnar nerve is exposed near the bones of the elbow, especially if the elbow is bent. You can probably locate it with your index. If you hit the ulnar nerve near the elbow, it can be felt in the little finger and one side of the hand.