There is one poinsettia, Euphorbia cyathophora (Wild poinsettia), native to North America and this USDA Plant Profile Map shows it grows naturally in Harris County. You can see the pictures below from our Image Gallery to judge whether this is the plant you have. On the other hand, if you purchased the parent plant, it is more likely that you have Euphorbia pulcherimma, which is indigenous to Mexico and Central America and therefore falls out of the realm of our expertise, which is plants native not only to North America but to the area in which they are being grown; in your case, Harris County TX. This USDA Plant Profile Map shows that this plant grows natively nowhere in North America. Both the native and the non-native belong to the Euphorbiaceae family and propagation methods should be similar.
This article from Floridata on the culture of the non-native poinsettia has this paragraph on propagation:
"Propagation: Take cuttings in summer. Use rooting hormone on 8 inch tip cuttings. An easier way is to take cuttings of woody stem about 18 in (45.7 cm) long, stick in ground and keep moist (not wet) for several weeks."
From herbaceous stem cuttings
From seed; sow indoors before last frost"
It would, then, appear that neither the native nor the non-native plant with the common name "poinsettia" can be propagated by placing cuttings in water.