I did a very brief check online of pain on the inside of the elbow, and saw something called "golfer's elbow," but the illustration doesn't look like where I was hurting. Then I saw tendonitis of the biceps, which makes sense to me--the pain seems to be where the biceps connect to the inside of the elbow. Many of the references were about the connection to the shoulder, but there were some referring to the elbow, too.
There's also an article about "distal biceps tendon rupture," which, according to the about.com article:
is usually an injury that occurs with heavy lifting or sports in middle-aged men. Most patients with a distal biceps rupture will have surgery to repair the torn tendon.
It's times like this that I hate the Internet.
I don't think I have a dbp, I didn't hear anything snap. Whatever it is, the likely cause is the insane push-up session we went through Thursday night at martial arts class. It's what you get when a 20-something athlete of a black belt stands in to run the class.