Clarify a bit for us here:
1. You missed OCI at your school or at the T20?
2. What kind of firm is the firm that you are interested in? I know you said "top BigLaw" but do you mean a branch office, main office, etc.? How many summers do these firms typically have?
Send out your resume explaining things ASAP. Missing OCI for BigLaw hiring is ill advised since many of the firms have very stringent hiring schedules. Furthermore, because many of these firms get mail bombed with resumes each recruiting season, many recruiting teams at firms only have the time to very briefly flip through resumes, trashing those that don't show great GPAs or great pedigrees straight off the bat. Its certainly still early enough in the game that you didn't "screw yourself," but I would get on things fast. I have a friend who basically did the same exact thing and got squeezed out of many of the firms she was looking at and would have been a shoe-in for. She waited until the end of Sept. to send out her resumes though, which was the big kicker..Good luck!