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A Reduviid (assasin) bug perhaps? They can give nasy bites. I do not think it is a diptera, because I do not think you would miss a Tabanid fly for anything else, Tabanids (or other dipterans) would not use a bite as a defense, beside, it is too late for Tabanids anyways. Also the way you discribe the scene (it turned around and than came the bite) does not seem to indicate a Diptera.