You can legally carry your CHL onto school grounds. You can go everywhere on the property except into a building which is the legal definition of "Premises" as far as schools and TEXAS CHL is concerned. The only thing that would restrict carry on school grounds is a "SCHOOL EVENT" taking place there and picking up your child from school is not an event. A CHL holder may have a gun on their person or store it in their locked vehicle if they must enter the premises. A TEXAS CHL is an exception to the federal and state "FREE KILL ZONE LAWS" as I call them. Many states allow their resident permit holders to legally carry in "School Zones" to one degree or the other. Out of state license holders are rarely, if ever, exempt from these laws.
Texas CHL holders as well as those visiting our great state can get very accurate and timely information as well as questions answered by very knowledgeable people at
http://texaschlforum.com/index.php . Also
http://www.handgunlaw.us/ has compiled information that can be verified thru links to Texas Department of Public Safety website which is the state issuing agency for the Texas Concealed Handgun License