That's interesting to hear. All I really know by Berg besides Piano Sonata are his two song cycles called "Jugendlieder" 1 and 2, his String Quartet Op. 3 and his Violin Concerto from 1935. I'd love to hear more of his piano music. It's such a shame that so little music is known by him.
A lot of music by him is well known; here's a list, although even this is probably not comprehensive:The following is a complete list of the compositions of Alban Berg.Jugendlieder (1), composed 1901–4, voice and piano, published 1985 Herbstgefühl (Siefried Fleischer) Spielleute (Henrik Ibsen) Wo der Goldregen steht (F. Lorenz) Lied der Schiffermädels (Otto Julius Bierbaum) Sehnsucht I (Paul Hohenberg) Abschied (Elimar von Monsterberg-Muenckenau) Grenzen der Menschheit (Johann Wolfgang von Goethe) Vielgeliebte schöne Frau (Heinrich Heine) Sehnsucht II (Paul Hohenberg) Sternefall (Karl Wilhelm) Sehnsucht III (Paul Hohenberg) Ich liebe dich! (Christian Dietrich Grabbe) Ferne Lieder (Friedrich Rückert) Ich will die Fluren meiden (Friedrich Rückert) Geliebte Schöne (Heinrich Heine) Schattenleben (Martin Greif) Am Abend (Emanuel Geibel) Vorüber! (Franz Wisbacher) Schummerlose Nächte (Martin Greif) Es wandelt, was wir schauen (Joseph von Eichendorff) Liebe (Rainer Maria Rilke) Im Morgengrauen (Karl Stieler) Grabschrift (Ludwig Jakobowski)Jugendlieder (2), composed 1904–8, voice and piano, published 1985 Traum (Frida Semler) Augenblicke (Robert Hamerling) Die Näherin (Rainer Maria Rilke) Erster Verlust (Johann Wolfgang von Goethe) Süss sind mir die Schollen des Tales (Karl Ernst Knodt) Er klagt das der Frühling so kortz blüht (Arno Holz) Tiefe Sehnsucht (Detlev von Liliencron) Über den Bergen (Karl Busse) Am Strande (Georg Scherer) Winter (Johannes Schlaf) Fraue, du Süsse (Ludwig Finckh) Verlassen (Bohemian folksong) Regen (Johannes Schlaf) Traurigkeit (Peter Altenberg) Hoffnung (Peter Altenberg) Flötenspielerin (Peter Altenberg) Spaziergang (Alfred Mombert) Eure Weisheit (Johann Georg Fischer) So regnet es sich langsam ein (Cäsar Flaischlein) Mignon (Johann Wolfgang von Goethe) Die Sorglichen (Gustav Falke) Das stille Königreich (Karl Busse) An Leukon (Johann Wilhelm Ludwig Gleim)Seven Early Songs, voice and piano, composed 1905–8, revised and orchestrated 1928 Nacht (Carl Hauptmann) Schilflied (Nikolaus Lenau) Die Nachtigall (Theodor Storm) Traumgekrönt (Rainer Maria Rilke) Im Zimmer (Johannes Schlaf) Liebesode (Otto Erich Hartleben) Sommertage (Paul Hohenberg)Schliesse mir die Augen beide (Theodor Storm), voice and piano, composed 1907, published 1930/1955An Leukon (Johann Wilhelm Ludwig Gleim), voice and piano, composed 1908; published 1937/1963 (Reich) & 1985 (UE) (2 versions exist: in G minor [1907]; in E minor [1908])Frühe Klaviermusik, published 1989Zwölf Variationen über ein eigenes Thema in C, piano, composed Nov. 8, 1908; published 1957/1985Symphony and Passacaglia, fragment, composed 1913Piano Sonata, Op. 1, composed 1907–8, published April 24 1911Vier Lieder, Op. 2, voice and piano, composed 1909–10, published 1910 Schlafen, schlafen (Friedrich Hebbel) Schlafend trägt man mich (Alfred Mombert) Nun ich der Riesen Stärksten (Alfred Mombert) Warm die Lüfte (Alfred Mombert)String Quartet, Op. 3, composed 1910, published 1920Fünf Orchesterlieder nach Ansichtkartentexten von Peter Altenberg, Op. 4, soprano and orchestra, 1912 (Altenberg Lieder) Seele, wie bist du schöner Sahst du nach dem Gewitterregen Über die Grenzen des All Nichts ist gekommen Hier ist FriedeVier Stücke, Op. 5, clarinet and piano, composed 1913, published 1920 Mäßig Sehr langsam Sehr rasch LangsamDrei Stücke, Op. 6, orchestra, composed 1914–15 Präludium Reigen MarschWozzeck (opera), Op. 7, composed 1914–22Drei Bruchstücke aus ‘Wozzeck’, soprano and orchestraKammerkonzert, piano, violin, winds, composed 1923–5Adagio, violin, clarinet and piano, arranged 1926 (arrangement of Kammerkonzert mvt. 2)Schliesse mir die Augen beide (Theodor Storm), voice and piano, composed 1925Lyric Suite, string quartet, composed 1925–6Drei Sätze aus der Lyrischen Suite, arranged for string orchestra, 1928"Der Wein" (Charles Baudelaire), concert aria, soprano and orchestra, composed 1929Four-part Canon Alban Berg an das Frankfurter Opernhaus, composed 1930Lulu (opera), composed 1929–35, orchestra part of Act 3 completed by Friedrich CerhaSymphonische Stücke aus der Oper "Lulu" (Lulu-Suite), soprano and orchestra, premièred under Kleiber in 1934Violin Concerto, composed 1935Vocal scores Franz Schreker: Der ferne Klang (1911) Arnold Schönberg: Gurre-Lieder (1912) Arnold Schönberg: Litanei and Entrückung from String Quartet no.2, 1912 Arrangement for string quartet, piano, and harmonium Johann Strauss II: Wein, Weib und Gesang, 1921There have been considerably more prolific composers, of course, but all of the above was achieved within a short life (like his idol Mahler, he died at age 50).If the OP knows more, however, this would indeed be of great interest; Berg was indeed a wonderful composer!Best,Alistair