Yes, you can tear muscles in any part of your body. The general rule of exercising and especially with regards to either repetitions or weight training, is that if something hurts, you should avoid that maneuver until your body heals. (this is much different from the "no pain, no gain" that we all used to hear in gym class!). Depending on the motion and how much stretching went into the specific pushup that caused the pain, you may have either strained or sprained the muscle, or affected it in another way. Stretching is vital, even to weight lifters, to make sure that the cartilage is adequately primed for optimal cushioning of the bones, and also to make sure that the muscle fibers are adjusted to the right level of tension. Proper stretching before exercise is an important part of any exercise regime to make sure that injuries, like the one that you had, are avoided. Your doctor
will be able to examine you and determine what the correct next step should be for complete treatment. Please speak to him or her, and do not do the maneuvers that cause you pain in the mean time.