My experience is the same as Lola's, with one exception:
"I have found that most will switch to Hochdeutsch when speaking to foreigners like us. Or they will use English. "
That's what I had read too, but that's not what I found. When I was in Luzern and tried to use my "German" (which is rudimentary), people did not switch to either High German or English, but responded in Swiss German. So, I quickly learned that for anything important, I started in English; they then responded in English. (Even my German teacher - a native speaker, from near Cologne, says that when two Swiss Germans are speaking to each other, she has great difficulty understanding them! Interestingly, she can understand Yiddish with no problem).
So, for your situation, have the allergy cards in German and English for the Berner Oberland. French won't help there; of course, if you are also going to French-speaking Switzerland, have cards in French and English. I agree with Lola that French is not regularly used in German speaking areas and vice-versa, and when it is, it is very much a third language after English.
Alas, Italian will only help you in Italian Switzerland. The languages of Switzerland are German, French, Italian, and Romansch, and they are VERY MUCH in that order of importance and prevalence nationally (regionally, as we're all saying, is a different story).