I understand people connected it with mountains, but was it connected to high altitudes in specific? (I think some people connected it to allergens in mountains.)
What I meant to say is did any ancient people say that high altitudes will make a chest constricted without mentioning allergens?
I can't think of specific chest constriction but the Greeks did have some notion that trying to climb Mount Olympus could be associated with blacking out, blindness and death e.g. the Bellerophon legend. They of course attributed it to the wrath of the gods at presumptuous mortals trying to trespass on their home. Although this is not necessarily specifically associated with altitude in general the specific peaks that are the home of the gods are generally the highest around so it may be a folk memory of altitude sickness. Therefore, my suggestion would be to look at similar legends to decide if this suggests the information that you are after, always bearing in mind the possibility that legends may have moved with the people who told them so that just because a legend is now associated with too low an altitude it doesn't mean it was always so associated.