Since you are not experiencing any pain you probably are not causing any damage. Many joints will “crack” when extended due to nitrogen bubbles bursting harmlessly in the joint space. This is nothing to worry about.
Pain, however, is a marker for a problem. The old saying of "no pain no gain" is not correct and should not be followed. As long as you are not experiencing pain, you can continue your push-ups and your bench-pressing.
We would, however, suggest that you have someone check your technique, and especially for bench-pressing to make sure you are not trying to lift too heavy a weight.
You're not alone. Take a look at a few of the questions related to this topic that other teens have asked us.
I'm 13. When can I start working out with weights?
How fast should I increase the weight I lift?
I'm a 13-year-old female. I'd like to start lifting weights, but no one thinks I can. What should I do?
For more information, check out these article:
Conditioning Your Body Properly
Posted 9-22-03