Try listening to it via headphones, if the highs sound distorted on the headphones then you know it's the recording. A better DAC might help, particularly one with tubes.
On the other hand, if the headphones do not sound distorted, then the problem is your speakers and you should consider better speakers.
Another possibility is that it's actually your room overloading (which does happen with loud music) and that can be frequency-specific. So if you have a lot of glass and/or bare walls, some absorbent acoustic panels would help, especially at the first reflection point on the side walls. If you have hard floors, then a very thick rug or carpet would also help.
