Ask Mr. Smarty Plants

First of all, I suggest that you read our How to Article, Container Gardening with Native Plants, with information about establishing and maintaining your container shrub.  One thing you should keep in mind is that plants in containers are more susceptible to freezing temperatures than those that are planted in the ground.  Their roots don't have the insulation of the soil to protect them.  You will need to remember to protect them during extreme cold.

Sorry, but we aren't going to be able recommend shrubs/small trees that exactly meet your criteria.  Some of the ones below reach a maximum height that exceeds your requirements, but they generally grow slowly and can be pruned.  Their shape may not naturally be what you are looking for (slender); but, for any of them, you can do some judicious pruning to keep them narrow enough for your purposes.  Some of them don't do well in heavy shade but will work in partial shade.  Although you don't say so, I suspect that you are looking for an evergreen tree/shrub to stand by your door, so here are evergreen possibilities for shrubs/small trees native to your area of Texas:

Ilex vomitoria (yaupon) will grow in sun, part shade and shade; here is more information.

Leucophyllum frutescens (Texas barometer bush) will grow in sun and part shade; here is more information.

Rhus virens (evergreen sumac) will grow in sun and part shade; here is more information.

Juniperus ashei (Ashe's juniper) grows in sun and part shade; here is more information.

Juniperus pinchotii (Pinchot's juniper) grows in sun and part shade; here is more information.

Juniperus virginiana (eastern redcedar) will grow in sun, part shade and shade; here is more information.

Sophora secundiflora (Texas mountain-laurel) grows in sun and part shade; here is more information.

Ilex vomitoria

Leucophyllum frutescens

Rhus virens

Juniperus ashei

Juniperus pinchotii

Juniperus virginiana

Sophora secundiflora