Does distorting at max volume mean that your track literally only distorts at max volume? If so that really sounds like a flaw in the playback system that your tracks are exposing. Most commercial audio systems, in my experience, can be made louder than than they're designed to handle. And the speakers and amps are different components that amp could overpower the speakers. Also they may well distort differently at different frequencies. It could be that your track has frequency content that happens to distort more readily at the top end of the playback system in question. I would guess the problem area is a lower frequency.
The other possible culprit is that your track is limited to 0db and you're hearing momentary >0db peaks. But, to be honest, plenty of commercial tracks peak over 0db and it's not readily noticeable.
On the other hand you might mean that your track is distorted it's just more obvious at max volume, in which case it's a production issue. You should always have a limiter at the end. Compressors can introduce distortion. Your samples might have distortion built into them.