I kinda have similar problems couple weeks ago, I went and got the battery and the chargin system check at a locol shop, they recommand to change the battery and the alternator. they should be able to do that for free (check with autozone or pepboys
like most people here say, round the time that your battery/charging system goes bad, crazy stuff happens.
but i only change the alternator knowing that my battery might be able to last a bit longer (which i'm not sure if i should do that or just replace the battery too).