AAARRRGGGHHHH! I hate it when I spaz out and hit the escape key three paragraphs into a training explanation!
adkoch, you sound like you have a leg strength discrepency. Been there, done it, went to SI joint hell because it wasn't attended to properly. What happens is that one leg is stronger and does more work, so the forces of pedaling will pull hips and SI joints and pelvic alignment in general all out of whack, and the hills would really bring that out. The easy test for this is to go to the gym, get good and sweaty warmed up, hit the leg press. A free weight press is better if you have one. Get the person who knows what they're doing to help you if you don't know how to push iron. Make sure your lower back is flat and your form is perfect, use the mirrors.
Do a warm up set or two- I like a twenty rep set for leg press or squats myself, and don't be a ***** about the amount of weight unless it hurts your hip. Then back the weight down and work each leg separately- you will be able to compare and tell if one leg is stronger very easily.
If this is the problem, the simple cure is to do exactly the same thing two or three days a week and train the weaker leg up to the same level as the sronger. You can also do a drill on the bike by outrigging one leg and pedaling with just the weaker- in a low traffic flat place. You may be able to check your legs against each other like that too, but the leg press is really obvious.
I am neither a sports medicine doc nor a physical therapist, just know a lot of stuff I picked up from coaches in different sports and my own PT. If your hip is really inflamed and painful, or this test really hurts in a bad way (red or white pain), see somebody. (it should be pink and blue with butterflies pain) The longer you ride with injury the longer it will take to get rid of it. And I could be totally wrong about what the problem is- but this is a cheap and easy fix for this particular malady.
Best of all, work that press and you will fly like a bird on the bike and sprint like a rocket. Leg strength rocks!

Lizzy

Before anybody complains, ***** meaning wimp is a slang diminutive of pusilonomous. It's not a sexist insult about women's parts.