Texas ended its state inheritance tax return for all persons dying on or after January 1st, 2005. So, until and unless the Texas legislature changes the law, which is always a possibility, you’ll likely not owe any Texas inheritance or estate tax.
If you move outside of Texas or own real estate in a state outside of Texas, however, you may be subject to another state’s inheritance or estate tax laws. As I’m only licensed in Texas, I can’t speak to the laws of other states and you’ll have to consult a licensed lawyer in the state other than Texas.