You may move in. Just don't wave your gun around. You will not be prosecuted for a righteous shoot if it happens in the apartment complex, but it will likely alarm some, and "threaten" others who hate guns; and you may be evicted for those reasons. But you won't be breaking any law, so long as you follow the Texas CHL laws....shall not... display, discharge, or possess, a gun, knife, or other weapon in a way that may threaten or alarm others
If you're from out of state, then the Current laws as of September 1, 2009 (clean version) (PDF) is highly recommended reading.