I run with my phone all the time. I used to have an arm band that it sat in but over time the bands would weaken in critical areas and make it hard to stay on my arm. I think it's because I bought crappy 10 and 15 dollar ones. Eventually I got tired of using them and just started running with my phone in my hand. It was annoying at first and it felt like it threw my stride off but I got used to it in about a week. I use my phone to keep track of my running pace and distance traveled with a few running apps. So far I've tried the nike and runkeeper one, both seem to have their quirks though. Primarily I run with my phone for the music and I use google play.
I used an armband too and although it freed up my pockets, I found it was uncomfortable and even a little constricting on my arm. That's really neat that you decided to start running with it in your hand! Do you find that you switch hands during your run when holding your phone? I know when I ran with my phone in my pocket, I was paranoid that extra 5 oz would offset my body, so I would switch sides halfway.
I actually just keep it in my right hand and I think that's just attributed to me being right-handed and always doing things with my right hand. The most annoying part about running with it in my hand though is the wire from my earphones going all over the place. To solve that sometimes I just run the wire into the sleeve of my shirt. If you don't mind the occasional looks this works great!