The short answer is- it is extremely unlikely that the mics are producing the distortion you are hearing. Although we don't have sufficient information to begin troubleshooting your problem, there is a high probability that what you are hearing is clipping. If you can see it in waveform, it looks like the top of the waves were cut off with a pair of scissors, with resulting flat tops, hence the term. When you hear it, it sounds like somebody squeezing a ball of Saran wrap, and it's not pretty. Clipping results when some component in the signal chain is overloaded, which means that you have to turn down the gain on the device feeding the overloaded component, or you have to turn down the gain on the overloaded device, or both. Any device can be overloaded because it is receiving a signal that is too hot, or because it is trying to produce more gain than it can.
Most recording gear has clip indicators, usually some variation on a red light or indicator. Some cheap gear can produce clipping before the indicator ever comes on, and some pieces of really sucky or defective gear produce nothing but clipping, like an old fashioned transistor radio. The process of sorting all this out is called gain staging. Most likely, you have to turn something down, and something else up. Also be aware of how you are hearing the music. Sometimes there actually is no distortion at all on the recording, but your monitor system or headphone amp is being overloaded, which produces the same effect. You can overload a mic and cause clipping, but that is way down on the list of likely causes. Most likely, there is a preamp in the recording system or the playback system which is clipping. Other issues can involve a blown monitor or headphone speaker. The most common offenders are cheap preamps, such as the ones found in most mixers or cheap computer interfaces.Good Luck-Richie