I have not had to travel since getting my Ostomy but In some hospital emergency rooms they have us take everything out of our purses etc… and put into a gray tub while going through the metal detector. They have taken my Ostomy scissors from my emergency bag anytime I go and if I bring that in with me so I’d assume they would do the same at the airport. If your bags are not cut already just cut a couple ahead of time for your emergency bag for the trip. 
I have not heard of TSA giving people trouble for having appliances unless they see a bulge they might wanna search you. I usually saw them take people off to a side room for that but I bet when they see it’s an appliance they are not going to mess around with you too much after that. 

Hi Rick.  I travel frequently (ie 8 or so flights per year) and have only ever had one "pat down", no shirt lifting.  It was a non-event, just told them I had an ileostomy and they patted gently around it.  All the other times, including international travel, I went right thru the scanner with no issues.  I am TSA pre-check, so not sure if that makes a difference, but I'm sure you will be fine.  Bon voyage!

@lynne Similar experience. It's a bigger deal in our heads than it tends to be in real life.

I would let the TSA agent know of my appliance before going through the scanner, or else they'd always ask about it after seeing the scans.

When they do a pat down, it usually involves you touching your appliance, and then you touch this paper, so they can test for explosive residue.

I do outline more of my experience and what to expect as part of THIS article.

Happy travels, @rick!