Ask Mr. Smarty Plants

The first place to go to find a list of potential dwarf evergreens for your Texas garden is our Native Plant Database. Use the Combination Search feature instead of Recommended Species. This will provide a bigger selection with much more choice to narrow down. The volunteers and staff at the Wildflower Center who maintain the database have partners in different regions to help with these recommended species lists based on what is easy to access in local nurseries.
Under Combination Search, select the following categories: TX, Habit – Shrub, Duration – Perennial, Light Requirement – Part Shade, Leaf Retention – Evergreen, and Size – 1-3 ft.

Some of the potential  plants for your garden include:

Ericameria laricifolia (turpentine bush)

Turpentine-bush is a broadly rounded 1-3 ft. shrub with profuse, small golden-yellow flower heads and dense greenery that turns golden in the fall. Leaves are clustered toward the stem tip and are short and leathery. They emit a tart lemony scent wen rubbed gently. If pubbed harder, the leaves get gummy and smell like turpentine. This small shrub bears numerous tiny yellow flowers in late summer and fall.

Leucophyllum candidum (Brewster county barometerbush)

L. candidum is related to the more common L. frutescens, but it is smaller, more compact, and has even more silvery, almost white, leaves. With its intense violet flowers that appear in the summer through fall in response to humidity or rainfall, it is a dramatic, eye-catching plant

Mahonia repens (creeping barberry)

Creeping Oregon-grape or creeping barberry is a stoloniferous, sprawling evergreen of stiff habit with small, fragrant, yellow flowers in drooping racemes, followed by showy, purple fruit. The leathery, holly-like, compound leaves are a muted green, some turning mauve, rose, and rust-colored in winter. The plant grows 1-3 ft. in height. A beautiful foliage groundcover for shade in the western mountains of the continent, creeping barberry has muted green leaves that are occasionally shades of pastel pinks, purples, and oranges. It thrives in good garden soil, but does not tolerate high heat or drying wind. Its yellow spring blooms attract pollinators and its berries attract birds.

Paxistima myrsinites (Oregon boxleaf)

Oregon boxleaf is a shiny, low-statured shrub, 8 in.- 2 ft. high, with small, glossy, dark-green leaves arrayed in pairs along ascending branches. The tiny, maroon flowers, appearing in the spring to the South and in summer to the North, are borne in axillary clusters. They are not conspicuous, but the evergreen leaves are attractive both in summer and winter.

And to answer your question about growing Agapanthus (a non-native), Kathy Huber wrote in the Houston Chronicle the following...

Many gardeners have found that agapanthus bloom best when the plants are slightly crowded in a bed or slightly pot-bound, but agapanthus flower poorly when truly overcrowded. Flowering may be sparse, too, the year following division/transplanting. Divide every four or so years, in spring or fall. General bloom time is May through July. Agapanthus thrives in a sandy soil enriched with humus. Good drainage is important. The tuberous-rooted plants adapt in sunny areas, those with morning sun and afternoon shade and those with winter sun and filtered summer sun. Water well during the spring growing season, especially while the plants are developing flower scapes. After blooming, water well and fertilize with bone meal or superphosphate. Water moderately in fall and winter, and fertilize again in early spring.