Q: I've noticed a clicking or popping sound coming from my right hip joint when I raise it to the side, and I tend to be far more flexible on my left leg. Are these two things connected? Should I be worried?
A: The clicking or popping sound doesn't necessarily mean you have a big problem, but it does indicate a muscular imbalance between the two legs and/or in the way you are using them.
Generally, people are born with similar hip sockets on both sides. You already stated that you are more flexible on the left side, so focusing on stretching out the right side is your first step. I strongly suspect the right hip has less rotation, tighter hip flexors and perhaps even some extra tightness in the turn-in muscles. (For some helpful exercises, see "How Turn-in Helps Your Turnout."
Also, try bringing the right leg into more of a forward diagonal when lifting it to the side and see if that decreases the popping. If it does, you need to rework how you are engaging the right rotators and tracking your legs. Work the turnout on both legs, not just the working leg.
If you don't see any improvements after trying these pointers, please see a dance doctor or physical therapist to be checked for a potential leg-length difference or any other structural challenge.