I'm going to semi-disagree with many of the answers on here, perhaps on a technicality:
Yes, standing is much harder on your bike equipment and does allow you to apply a signnificant amount of torque to the frame and components. For normal cruising riding, staying seated is likely the best route.
Instances where standing is required:
-Offroad riding (MTB) - often quick burts of torque are required to quicky accelerate, such as to gain speed for clearing an obstacle. Standing is the only way to obtain these levels of torque.
-Offroad riding #2: On hardtail mountainbikes, rolling over obstacles and taking jumps will hurt your rear and tailbone if you do not stand up. So when pedalling over obstacles, standing will often be required to prevent injury. This also will increase traction, as your body acts as the rear suspension.
-Onroad racing- Road racers often maximize their output and endurance by alternating between seated cranking and standing high-torque acceleration.
There are other scenarios as well, but in your specific situation, it sounds like you should try to remain seated as often as possible. You may have shifter alignment problems or some other drive train problem that could be exacerbated by high torque pedalling, and having a part fail while applying standing-level torque can be painful (trust me here!)