I'm actually going through something very similar. I'm almost certain I've strained/pulled/injured my hip flexor, which is like a series of three muscles connecting your hip to pretty much everything else. My pain is located just below my hip, definitely not my groin, cuz I know what that's like and this isn't it. It's very sharp, almost arthritic if I had to guess what arthritis would feel like. It's very hard to stand on that leg alone, and standing up from a seated position hurts. Walking isn't too bad, except that I have a compensatory limp that is kinda noticeable.
I think I just pulled it by jumping right onto a treadmill, on a very cold day, with only shorts on my legs, and not having stretched at all beforehand.
I didn't run for like a week, but it had improved, so I tried running on it and it was worse the next day than it had been at the start. So then I stayed off the treadmill for another two weeks, tried running again, and it was bad again.
It's been four weeks now and it's still not healed. I walk from the train to work (6 blocks, maybe 7), so it's impossible to really rest my leg 100%, but Bengay helps a little, and I've been doing ice after work (in case there's inflammation) and heat at bedtime (to help with the healing).
If anyone has any advice on this injury, I would love to hear it. I already know that I should probably go to the doctor, but not if I can wait it out on my own.