iPhone 5 is lagging

I got my iPhone 5 a month and a half ago. It was working perfectly until just this week. I noticed it when I was playing a game (Subway Surfer) when the phone didn't respond to my swipe motions. This is unusual, because I originally found the iPhone 5 very responsive (much more than my old 3GS). However, now my swipes lag with every game I play. Also, it lags in telling me my battery life. For an entire day, I will have 84% battery life, the number never changing, when all of a sudden, the number will instantly change at the end of the day to 3%. It's really weird! My phone also lags to recognize that a charger was plugged in (it took a full minute to recognize my charger). Occasionally I won't get all my texts and calls, but I think that's a problem with AT&T. I've never dropped my phone, and I don't have apps running in the background. I don't know what to do!