Dr gave 3 courses of augmentin for confirmed strep that kept returning right after course ended. now on clindomycin 300mg 4x/day. should this work?

Not necessarily: You should have the streptococcus that caused the infections grown in medium and tested for a panel of antibiotic sensitivities, you might have a resistant strain causing the recurring problems, although Clindamycin is a good second line antibiotic...

Some questions: Are you disposing of your tooth brush between infections or retaining the same ? Is your partner or other close family member a silent carrier or has this even been studied ? Has your treatment course lasted 10 days or been shorter ? Strep is sensitive to the penicillin drugs, but you can be re-infected at any point you clear but are exposed. Clindamycin is a good drug, but there are other issues