This sounds exactly like you have tight hip abductors and hip flexors, which is causing pelvic tilt and lower back pain. This is especially a problem if you sit for long periods of the day and will become apparent when doing exercise, especially running.
You need to stretch you hip abductors and flexors and strengthen them.
[video="youtube;HaQFZ8TOUfA"]https://www.youtube.com/watch?v=HaQFZ8TOUfA[/video]