Default Lag or Screen Problem?

Hey guys. I own a Sony Xperia U and I've had it since September of 2012. The phone has had its fair share of being dropped. I've also rooted it and I have tried different ROMs. I feel that my touch screen has a problem. I have a bit of difficulty when writing new messages, when I tap on a letter, sometimes it doesn't respond. Same with playing games, say for example, Flappy Bird. Whenever I tap, it doesn't always respond to my tap. I'm saying that I can only "feel" that it is a touch screen problem because I also think that it could simply be lag? I've tried using different roms, going back to stock but the problem persists. I've tried modifying the sensitivity of the screen but I don't think it really did change. What do you guys think? Is it the touch screen itself or could it be lag? What do you guys suggest? Thanks!
Sony Xperia U!