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The rabies vaccine is considered effective if given up to 14 days after an exposure. Here is the official prescribing information for the vaccine. Specifically, I bring your attention to the following section:
Post-exposure efficacy of Imovax Rabies vaccine was successfully proven during clinical experience in Iran in which six 1.0 mL doses were given on days 0, 3, 7, 14, 30, and 90, in conjunction with antirabies serum. Forty-five persons severely bitten by rabid dogs and wolves received Imovax Rabies vaccine within hours of and up to 14 days after the bites. All individuals were fully protected against rabies.
http://www.fda.gov/downloads/BiologicsBloodVaccines/Vaccines/ApprovedProducts/UCM133484.pdfWhile the risk from a non-bite exposure is considered much less than a bite, I do believe that the current CDC (USA) recommendations would be for you to receive the vaccine.