Ostiboy,
I've flown quite a bit since surgery, 6 flights in the past two weeks including Dallas. Your bag will show up, pretty detailed, when going through the security checkpoint. Expect to be stopped. When I am I say "my ostomy bag right?" You'll then be asked to rub your hands over the area and they wipe your hand with a towelette. They put it in a chemical detector and give you the go-ahead when the results come back clear. I've never needed the card. It's just one more thing to fumble with ID, boarding pass etc. It's very discreet and fairly quick. Remember, it may be uncomfortable for the TSA agent also. They have been more than accommodating. My only problem was in the Netherlands when there was a language barrier. After answering "Ostomy bag" numerous times I gave the answer "S*# bag". Needless to say I was pulled into a room for a quick visual check. Even there they were very accommodating and apologetic.
As for asking for a seat next to the bathroom, if it makes you feel better, do it. I usually fly Southwest and pick my own seat on an aisle and near the back. On any other airline I book an aisle seat. Personally, I wouldn't feel comfortable telling someone about my condition if I didn't have to.
10 minutes before boarding I head to the airport bathroom to empty and check the pouch seal. Carry a supply bag containing EVERYTHING you need for an emergency bag change. I had that incident once. Upon seeing the seepage beginning I panicked. I took a deep breath, calmed down and was done within 5 min. Depending on what appliance you use bring a chemical "hot pack" to hold over the new bag. This is a typical bag used as a heat pack for a sore back or similar situation. Key to this process is to expect it to happen. If you do that you'll already have a plan on how you will handle it and just react. This should lower some of the anxiety.
Over the years I have become a "bag petter", gently wiping my bag to push any waste down into the bag. If the flight still has a couple of hours to go I may head to the bathroom. One thing I suggest is to put toilet paper on the bottom of the toilet before emptying. Urinate after. As airline toilets work with suction, you will find yourself pushing the flush button many times without any liquid to help move the matter. This happened to me once. Walking out after flushing 4x was pretty embarrassing. About half the plane stared at me with the look of "Are you okay/is it safe to go in there???"
I found flying was a lot easier than I figured. Keep that supply bag with your carry-on and you'll be fine.
Don't worry. Enjoy your trip.
SharkFan