It’s possible, sure. Apple Motion (their answer to After Effects) is needed for that level of compositing. The shirt would need a patch of green with tracking markers. The tracking markers will need to be removed in the editing process.
This is not something I’d recommend for a total novice. It’s not a plug-and-play process and requires a LOT of effort to get it right. If you are that determined, get the shirt printed now and do some extensive testing and practice renderings before you head off to New Orleans. Learn the ins and outs of this type of composite so you aren’t surprised or disappointed when you try it for real.
I’d really recommend you find an alternative solution. This is a tall order for entry-level.
One thought would be to take a series of photos of your family with different reactions (laughing, pointing, amazed, puzzled, looking left, looking right, etc.). Print each one on an identical shirt stock. Shoot your own reaction shots to different things you see, wearing the shirt that matches or appropriately compliments your reaction.