No, neither of us are mixing the cannons and mortars. Follow my link to the Columbiad article. Those big guns were definately cannons, not mortars. They had a range of over six miles, so it is resonable that the shell you found was fired from across the river. Remember that the sights on artillery in those days were just overgrown rifle sights. Indirect fire was not used until the Spanish-American war. It is possible that the half shell you have resulted from it bouncing off its target in the river after smashing whatever it hit.
Try to find the exact diameter of the shell. I'm sure there are archives that provide detailed movements of guns during the war. You have a nice artifact. Try to find out more about it.
Anything that size in Texas during the CW would have been on the coast, probably at the mouth of a river to take out the ships offshore unloading troops to the smaller boats, probably row boats, to come up the river.
There were small paddle wheelers that traveled the Trinity, but they would be sitting ducks no matter what was used. Only the smallest of boats could turn around. Take one out and the rest would be dead in the water because they probably couldn't get around it.
Once in the river the small boats could be taken out with small artillery pieces which are quicker to load.
The more I've looked into it the more I believe it's not from the CW but was Mexican. Santa Anna had the army to move and man a piece this size.
It probably wasn't as heavy as the CW pieces since it wouldn't need to be used at long range, Texans didn't have but a few cannon to fire back with and they were small.