Silvia. You don’t say how many nights/days you are in Bavaria and how many you have for both Switzerland AND Sud Tirol. You don’t say where you’ll fly into and out of.
Even if you spit it kind of evenly, 7 Bavaria, 7 Switzerland and 6 Sud Tirol, there’s a lot of traveling that will eat up time from your 20 days.
I agree with Zermatt and the Matterhorn (must sees on our only Swiss trip), but with limited time, I’d say 4 nights in Berner Oberland (Wengen or Murren) along with 2 nights in Luzern.
Sud Tirol could either mean the Dolomites between Ortisei and Cortina d’Ampezzo OR the area around Meran/Merano and west of Meran/Merano.
Since you would have seen the Alps in Bavaria and Switzerland, for the Sud Tirol, I’d head to the Val Gardena, Dolomites, as they are vastly different than the alpine scenery in both Switzerland and Bavaria. With 6 nights you can see a lot, plus take day trips to Bolzano and/or Bressanone.