If an e coli urinary tract infection showed to be susceptive to norfloxacine, why did the doctor prescribed me ofloxacine, I feel its not working.

Similar drugs. These two meds are very similar and reasonable substitutes for each other. If treatment for a UTI does not result in improvement after several days then a reevaluation is warranted.
Cousins. These two antibiotics are "cousins" as they are both in the same family, the fluoroquinolones. If one would work, the other most likely would.