Welcome to the Forum, Nakla.
Looking over your list of chamber music likes, I can suggest a few directions:
If you liked the Tchaikovsky quartets, you should definitely check out the two by Alexander Borodin.
Shostakovich has 15 devastatingly beautiful and haunting string quartets. If you liked the Shosty Trios, you should turn to the Quartets ... and any other chamber music from this Russian master.
Both Dvorak and Brahms have string quartets which may prove of interest. I tend to find those of Dvorak more interesting, but Brahms's chamber music which features the clarinet is indispensable and remains a "must hear".
Mention of Franck reminds me he has a wonderful cello sonata and to recommend chamber music of Gabriel Faure. And the string quartets of Frenchmen Debussy and Ravel (one each) prove major pieces to make acquaintance with.
Beethoven has tons of chamber music, but look at his sonatas for violin and piano. (They're generally identified as "violin sonatas".) Prokofiev has a couple of these, too. These works will well complement the cello and piano sonatas.
Rachmaninoff has a great Sonata for cello and piano. You must hear this one!
Alas, poor Bruckner left us too little chamber music. But he makes up for it with a dozen great symphonies, which, if you continue pursuing classical music, you will eventually come to. The Seventh Symphony is a supreme masterpiece, one of the greatest classical music works in the catalogue. Certainly not chamber music, but worth a listen for a change of pace.
If you want to enter the "challenge" mode, you might try the Schoenberg string quartets. They will provide about as good an intro into the "modern" movement in music as anything out there -- not too bizarre, still grounded in the Romantics like Brahms, but offering new paths for the ears to follow.
Another mode of "challenge" mode will be to pursue the String Quartets of Franz Schubert. These are heavy Romantic pieces, not for the faint of heart, and their deepest beauties may take years to discover, but they remain pinnacles of musical art. Not easy, certainly, but worth the time and effort to listen. Schubert has a number of other great chamber pieces as well. In his short life (he died aged 32) he created enough music to last anyone's else's lifetime. A true master.
So ... there are a few recommendations, all more or less keeping you in the same area of reference you are familiar with, but expanding your ears a touch and introducing worthwhile paths.
Path will lead to path. Just keep your ears (and mind) open, and tread onward. There is nothing quite like this journey. I've been on the paths for over half a century now, yet I suspect the hidden vistas are vast. I have no intention of stopping now.
