IPhone 5 :: Keeps Missing Calls And Sending IMessages?

for the past five days my iphone 5 has been acting funny. My friend called me three times before I actually heard a ring and picked up. He told me that he kept calling, but I wasn't hearing anything. Afterwards, when I looked at my phone history, it says I had indeed missed a bunch of calls. The next day he tells me the same thing, except with Facetime. When I look at my history, it says "Facetime answered on another advice." It says this multiple times, especially when I do not hear my phone ringing. I do not have facetime on any other device besides my iphone 5.Â

At first I thought it meant that my phone was just acting weird and that the place I was at had no signal at all, hence why it took my friend three tries to reach me. But then the weirdest thing happened. Yesterday, my friend called me while I was driving. I wasn't picking up so he called again. When I got home, I called him back. Everything was fine. But when I looked at my imessage history with this said friend, it showed a message I never even sent! It was in English, but I definitely am sure I never sent that text at that time because 1 - I was driving & I knew where I was during that exact time and 2 - I don't even text that way!Â

This is odd. My phone is always physically with me and my phone is NOT jailbroken. I know it's not a glitch because after my phone sent that text message, I had a feeling my phone was being hacked or something! I just changed my icloud password, does that do anything? If someone has access, will it stop now that my password is changed? Do I take it to the Genius Bar?