Texas is a really cool state in this regard. Fom what I have read they allow you to base a marriage license on an existing marriage license. What this means to me is that they will issue a second license even if you already have one.
To find out for sure contact the register of deeds in you county. They may send you somewhere else but it is a good place to start.
See the following site:
"Renewal of Vows or Secret Marriage Remarriage:
According to the Texas state laws, a county clerk must issue a marriage license to a couple who is already married to each other. "
You might consider telling the minister or priest officiating at the ceremony that you are already married in Texas. He or she can still perform the big ceremony but would not have to file any paperwork in VA.