The most important thing for you is proper form...if you're not doing an exercise properly, you're not going to get results, and you're going to get hurt. Be careful about the pushing through pain thing...you have to know the difference between soreness and injury. If you're 15 years old and 110 pounds, you probably don't yet. Don't try to impress anyone with how tough you are. The results will come if you stick to it, but you can't stick to anything with a herniated disc or torn labrum.
At your size, you'll probably have trouble gaining weight. I recommend that you go to stronglifts.com and follow the 5x5 beginner program for three months, focusing on form. Once you have gained some experience and maturity in the weight room, you could try GOMAD (look it up) to gain some weight. Be sure to keep in touch here and with your doctor.
On the other hand, maybe being a big weighthead is not your thing. There are a tremendous variety of bodyweight exercises which can get you very strong. They also have reduced chance of injury, which is important for a beginner and/or someone who doesn't have access to a real gym.