First of all, don’t send him any more screen shots of other guys texting you. It will give him the wrong idea. Especially if he’s shy. 😉
Second, I think you should let him be the one to ask you out, and the reason is that guys really feel good about themselves when they chase and win a girl over. When you ask him out, you take that opportunity away from him. In addition, if you do ask him out, go out, have a great time, and there’s no date forthcoming from him, you’re in a worse situation than now because now you’re asking yourself why he’s not asking you out after a good time at a frat party AND a good time on a date.
Third, this doesn’t mean you should do nothing. Flirt with him, which is the way he will know you’re interested, and you’re giving him something to chase after. You can figure out where he’s going to be and show up and flirt, but don’t chase him — let him be the one to do that.
Hope that helps! Let me know if you have any more questions.