I've gotten to the point I can swing hard enough that I'm in danger of hurting my shoulder. I felt like the ball almost came out of the socket earlier today. I will need to take lessons.
I'm worried though, if I ever get into a fight, that the person I hit will be permanently disfigured or possibly killed.
It's possible you need more "base" in punching. At this point, you should not concentrate so much on power, instead, work on your form and volume of punches. You will build strength and endurance through this conditioning. Worry about power after you build this base. If you are naturally powerful, you will have it now anyway, so don't work at power all of the time. Are you punching a heavy bag, focus mitts, sparring and / or shadow boxing?
It sounds like the pain is coming from your rotator cuff. Are you throwing a straight cross, hook or uppercut when you feel the pain? All of them? Is your cross straight? An improper form might contribute to injury. When you throw a straight cross, rotate your thumb down while tightening your fist more before impact. Also, from my experience, certain resistance exercises combined with boxing / punching range of motions can cause more wear on your rotator cuff. Limit those particular *heavy* resistance exercises, and do lighter weight / more reps, or eliminate those particular exercises so you do not injure your shoulder in boxing.
Strengthen all of your muscles in your shoulders, chest and back so you lessen stress on your rotator cuff involved in the punching range of motion.
Remember to pivot your shoulder and hip into the punch. Also, build leg and core strength. A lot of power is generated through the legs.