Is it possible to catch a bacterial infection (eg. streptococcus), while already taking antibiotics?

I had been taking antibiotics for a suspected strep throat, which then turned to be a false alarm. But midway (after 9-10 days of antibiotics), I came into contact with an infected person and it seems that now I REALLY have a strep infection (extreme sore throat, high fever, malaise, etc.). I still have 5 more days of antibiotics (Dalacin 600mg x 3/day), but if the infection has just started, should the antibiotics be extended to 10 more days (ie. amounting to 20 days in all since the bogus infection treatment had started)? Or should I have my antibiotic changed? (ie. could the strep bacteria (if that is what it indeed is!) have "hatched" already immune to antibiotics since they got incubated within the antibiotic environment? Help please! It's a dilemma, not even my Doc can figure out ;-( (he said the strep test won't be reliable in this case, either...)