Reply: It's really hard to make the CM-311AE distort unless it is not getting enough voltage from the transmitter. The maximum SPL that the CM-311AE can handle at 1 kHz is 140 dB SPL with 3V DC, and 148 dB SPL with 9V DC. A screaming voice can reach 140 dB SPL with the mic touching the lips.
Something to check: The transmitter input can be overloaded by a hot mic signal. Inside most transmitters is a gain potentiometer. Using a small screwdriver, turn down this pot all the way and see whether the distortion stops. Also make sure that the receiver level is set so that the receiver is not distorting (clipping), and check the PA mixer's input trim or gain control to make sure that the mixer input (fed by the receiver) is not clipping.
If all else fails, sing a little quieter or move the mic about 1/4 inch or 1/2 inch farther from the mouth