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I did a calculation of what is the average rainfall from landfalling tropical cyclones on the Upper Texas Coast. I was only able to find the highest rainfall total for 44 out of 74 tropical cyclones that made landfall. The lowest was from Tropical Storm Chris in 1982. It only dumped up to 0.96" in Texas. The highest was from Tropical Storm Claudette in 1979. It dumped up to 45" of rain.

Statistics

Average
15.24"

Median
14.02"

By Quartiles
25th Percentile
7.73"

50th Percentile
14.02"

75th Percentile
19.61"

95th Percentile
33.4"

99th Percentile
43.14"

Sources:
http://www.hpc.ncep.noaa.gov/research/txhur.pdf
http://www.hpc.ncep.noaa.gov/tropical/r ... nfall.html

With this hurricane season, it is not only wind and storm surge we should worry about. We should also worry about heavy rain. Usually fast moving storms dump less rain, but there are exceptions. Hurricane Floyd in 1999 was fast moving, yet it dumped 25 inches of rain on North Carolina, despite moving over 20 mph. Hurricane Ike dumped 12 inches of rain despite moving at 18 mph. In those cases, they were interacting with a trough or cold front.