Some of the locals will offer better advice than me, but when it is this fresh, we work the southern end where the salinities are higher.
It takes a lot more skill to catch fish with under 2 parts per thousand near Hackberry than it does in the 10 parts per thousand near Cameron.
See the links for salinity near Hackberry and near Cameron:
http://waterdata.usgs.gov/nwis/uv?08017095
http://waterdata.usgs.gov/usa/nwis/uv?site_no=08017118
If the forecast holds, conditions might be right to fish the beach.