Hey Jennifer,
I had the same thing going on, right side compensating for my bad left hip as I shuffled down the sidewalk. Dr. Su resurfaced my left hip 10 days ago, and from about the second or third day when I stopped the pain medication, my right side has not been compensating for the left and feels great. One of my PT's at the HSS, Liz, caught me trying to use the right side to drag the left side along, and was quick to correct me and teach/prove to me that I could walk straight up and normally without a much of a limp at all. That was immediately after the surgery. Day 10 today, I am whipping around the house alternating between 1 & 2 cruches, and putting a few minutes on the treadmill as well. No pain in the new hip or non-operated hip & knee anymore. I am extremely happy with Dr. Su and his staff, you could not ask for better.
Best of luck,
Todd