I want to warn you now that this post doesn't really tell you how to cure compensations, how to identify them, etc. I just want to share my experience this time and stress the importance of finding/fixing your compensations before they become injuries.
We all strive to have this glorious balance in our bodies. But we compensate when something's wrong. And I mean everyone, not just dancers. It's mostly innate and unconscious - think about it. If your leg hurts, you compensate by putting more weight on the other leg. Soon, your other leg is tired. Vicious cycle, right?
I tend to hold my tension in my shoulders. Whenever I get stressed out (mentally or emotionally - not physically!), my rhomboids and upper traps act up. I feel it immediately (which is unusual, but I've come to be very sensitive to warning signs) - I start to slouch and tense when I'm sitting, my shoulders rise up a bit, my pecs get tight...and bam, I feel a pull in my upper back between my shoulder blades. As soon as I get to that stage, I stand up, roll my shoulders a few times, maybe get a snack or walk around or breathe deeply to relax, and change the position I was sitting in and I'll feel better within 5 minutes. Unfortunately, I've got other compensations - my pelvis is rotated, causing a lot of tension in my left hip flexors (front of your hip) and pain shooting down my left sciatic nerve (back of your hip).
Compensation is one of the worst enemies a dancer has. Example? I can tell you right now that if you get shin splints (unless it's completely hereditary), it's probably because you don't get your heels all the way down to the ground when you land a jump. You put so much tension on your calf muscles to keep your heel off the ground that the muscles on your shin feel the pain too.
The one thing I can think of that causes pain and compensation patterns in muscles is lack of education. If you aren't taught how to use your muscle in a way that won't hurt it, you probably will use it wrong. Based on our primary, survival instincts, our bodies want to find the easiest way to do everything. All muscle movements are about efficiency. Dance is not efficient. Everything (almost) dancers do goes against those basic instincts. If your teachers don't tell you what muscles to use and train you to use those muscles, your body will instinctively use the path of least resistance. When you do a tendu to the front, you want to push your toes out first, right? Ballet tells you to push your heel out first, right?
There are so many things I wish my teachers had drilled into me a long time ago. I guess I wouldn't have understood as a child, but if my teachers had said and enforced things like 'don't clench your butt when you're standing with your feet turned out' or 'don't let your arches drop/don't let your feet and ankles roll in,' my current life would be so much easier. I've found that a lot of my training in college is just trying to break bad habits I've developed earlier in my life.
The only thing I can really tell you to do is go to a good kinesiologist, physical therapist, athletic trainer, massage therapist, etc, who can #1 fix you, #2 tell you what's wrong with you in terms you understand, and #3 tell you what to change and how to change it so you don't injure yourself (again and/or more seriously). It's worth the money, time, and effort to find these things out early - or if you already have pain, you need to figure it out immediately. Don't just go to a therapist/doctor to get fixed - ask questions and find out why you're hurt and how to change that. Don't go on dancing in pain. Don't let your future be riddled with pain. And most of all, don't let your current habits become future injuries.