Standing to pedal is extremely tiring - should it be this difficult?
Standing up on a bike, especially when you lack fitness, is a good way to go "anaerobic." Put simply, that means your body is working so hard, it can't get enough oxygen. You can only do that for a short amount of time, which for most people is in the range of 10-30 seconds. Then the lactic acid build up in your muscles becomes too painful and you are forced to ease up.

The solution is simple. You need more strength and fitness. If you like to ride fast and/or climb hills, you can't avoid the anaerobic zone completely, but you can move it a little farther away by getting good fitness. Keep riding, and keep riding hills.