Of course you can do it! You'll want to make sure you choose plants that will tolerate shade. Think of the balcony as though it was a real garden. Gardens have paths bordered by planting beds, shortest plants up front, arranged so there is a pleasing contrast and harmony of leaf and bloom. You can mimic this effect with your containers. You'll want a couple tall plants in big pots - like tall shrubs, small potted trees, maybe a nice trellised vine. Then some lower plants like small shrubs or perennials in medium pots, and small pots with annuals or succulents or whatever to fill in. If you arrange these with the tallest plants in the back, you create an effect similar to a planting bed. You may also want to consider some window box type containers on the railing or on the floor along the edge, and some tables or plant stands to elevate your favorites up off the ground.
I found this on Google, thought it might be useful to help you choose plants. I have a balcony garden in hot & humid Tampa but my conditions are probably pretty different than yours in Texas.
Shade Tree Gardens