Perhaps media whore is a little strong. How about drama queen?
The only drama queen here is Barry Bonds and his “I’m a victim of the racists media” act. Schilling goes out of his way to avoid press coverage. If you knew anyhting about the idiot press in Boston (especially the hacks at the Globe), you wouldn’t blame him. He’s also had issues with ESPN in the past. He communicates with fans through a blog. The Dinosaur Media hates this, so they brand him as things like a “media whore” or a “drama queen”. Schilling’s a decent guy who sometimes speaks before he thinks, but he is neither of the things you described him as.