Tonsils swollen/pus pockets/very sore throat. lab results said "moderate beta-hemolytic streptocci, not group a isolated." is that not typical strep?

Yes and no: By typical, i guess that you mean the kind of strep that should be treated with an antibiotic. The reason for antibiotic treatment of group a strep is to prevent you from getting rheumatic fever as a consequence of the strep infection. With non group a strep, you have have to worry about rheumatic fever and so antibiotics aren't required for prevention but you should talk to your doctor about it.