If you really like impatiens, it might be worth your while to search out some of the newer sun-tolerant impatiens. There are varieties available that will take full sun---even in Texas' summer heat!
However, you might consider looking at other white-flowered annuals, such as vinca (Catharanthus). If you do an advanced search in our plant encyclopedia, you can search by flower color to get a list of possible plants to consider.