A story from a male friend: long before the scanner nonsense, his genital piercing set off a handheld wand (not the WTMD), and the TSA required him to submit to a visual inspection to resolve the alarm. I don't know if that's what they'd still do, but they didn't touch him in any way.
The piercings you have would definitely be picked up by the scanner, and a healing ampallang is not something you want to jostle around too much, so I'd err on the side of caution and refrain from flying until you're further along in the healing process.
I don't care about showing it. But I wouldn't want it to have it jostled like you say. I especially would want to avoid the clip from the bag hitting the side of the piercing. That would hurt and be bad. So I think I will not fly for a few months.