Yes, that's the hip flexor in the front. I don't know the name of the muscle in the back. Like anthemracer said, it could be the result of leg length discrepancy. Though I've done just about the same thing XC skiing which was a pulled ligament or tendon - took a year to heal. But that's not likely from such an low impact exercise as biking. Since it seems to be getting better the more you ride, I think it's just a matter of getting those poor muscles used to biking. Nothing really works your hip flexor like biking, so it's no great shocker that it's sore. I don't think it's a saddle issue. The pain in back could be referred pain from the pain in front, which would be why they seem connected.

Things to do: Try doing crunches with your calves up on a chair or couch and your hip angle at about 90°. See what that feels like. Watch your knees as you ride. Are both of them directly over your pedals? Do either of them describe a sort of circle or ellipse as they go up and down? Half way through your ride, get off and stretch. Take 600mg ibuprofen about an hour before you ride. Sometimes if it's an issue of swollen tissues, the ibuprofen can knock that down and allow things to heal. But in general, if it doesn't keep getting worse, and in fact gets better, don't worry about it. Keep riding and it will keep getting better.