The hot sun sure can do things to plants if they are not sun-hardy. What I mention here I have no idea about how hot a sun they can stand but they are sun-lovers for your zone.

Crape Myrtles....come in dwarf sizes all the way up to trees
Ligustrum
Primrose Jasmine
Texas Sage
Burford Holly
Chinese Holly
loquat
Flowering Pomegranate
How about a Japanese Yew in a container
Pampas Grass....cut it back to suit
Pygmy Barberry
Dwarf Abelia
Cotoneaster
Plumbago.....everytime I see that word, I think of an aching back

The big thing still to consider on balconies is the wind.
If your apartment is open to winds of sort, it could play havoc with whatever you put out there. Winds dry soil up much faster than any sun that might be high. More water would definitely be required.

I'm glad you asked this. I live in Virginia, not as as dry as Texas but our summers can really bake the hide right off of you! I'm starting a veggie container garden this year and we face due west with NO shade.......NONE. I'm putting in some beans, cucumbers, some hearty heirloom tomato plants, peppers.......sun loving plants and I'm praying our abundant sunshine isn't too much of a good thing. I'm thinking about maybe building something like a trellis which can be moved to offer some protection from the sun if it gets too intense after 4:00. Maybe you could put in some dwarf sunflowers? Nice color and you can feed the birds during the winter!

The heat is a ***** but the real problem is often drought. Aim for bigger containers (12' at the smallest) and you can try tomatoes again. Anything smaller than that will have to be watered like crazy.

For the window boxes, you might try purslane, portulaca or ice plants - all blooming succulents. They do well even in south Texas (RG valley, grew up there) so they should do all right for you. You could also try bouganvilla, which is gorgeous and tolerates heat and drought and will shade the rest of your area. (You might have to protect it during your winters, though.)

A lot of mediterranian herbs will flourish in your space... rosemary, lavender, oregano, possibly sage and thyme too sinse your area is dryer and has colder winters than us on the coast. Basil will take sun and heat, but it is a thirsty plant so take note.

best of luck!

i also have a west facing balcony. asparagus fern and vincas work really well. those have been my two favorites for the west side.

I have a west facing balcony as well. I live in California and everything used to bake in the afternoon sun. Watering became real tiresome. So I got rid of everything and got one plant. I got a variegated bower vine and I am letting it spread.

Argh, i have the worst problems... My
balcony faces west and i cant even enjoy sunset because another buliding blocks in front.. I probably only get crazy drought hot sun
that starts from 1PM to 3PM. My morning glories never bloomed, even if they tried they dont fully opened.. I dont get any morning sun, only noon! And sometimes plastik or rubbers melt, and my feet burns when i step the floor... I have no idea what im going to plant now. But strangely a group of Johnny jump ups germinated, lol

I have a west facing balcony in Tempe, AZ, but there's a solid wall on the south side of it and a solid overhang. I've had an elephant bush (portulacaria afra) that withstood the west summer sun just fine and grew like a weed. I now have a variegated one that is a lot more sensitive to burning, but I hang it behind a pillar on the north side of the balcony now. I also have a string of bananas (senecio radicans) hanging on my balcony, but it hasn't been through the full direct summer sun yet so we'll see how it does. My Aloe and Plumeria seem to handle it ok too surprisingly.

Most of my other succulents don't seem to like being in that direct summer sun for more than a couple of hours though. I learned the hard way burning a Congo Aloe, Stacked Crassula and Golden Sedum on my table which gets direct sun for a few hours. I think I might have to resign myself to a squatty Cactus of some kind for that spot.