I hereby correct myself. According the the Texas Secretary of State, the runoff date is July 31, 2012. I'm going to ask my SREC committeeman and committeewoman about getting an absentee ballot and how to get it counted. Normally ballots mailed from within the county within one is registered are not counted unless the voter is 65 or over or disabled.
http://www.sos.state.tx.us/elections/voter/2012dates.shtml