When you are showing off the shirt, then the designing is in the past, so 'I designed' is more natural in that context. I doubt if there is any difference between BrE and AmE there.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Oceanatali I would say "I've designed",because I want to put an emphasis on the action happened at an unstated time in the past.That is not the purpose of the present perfect tense.
Oceanatalican I say "I've designed"?Not there. But you can do this: