I desperately need a new phone but don’t want to loose Tik Tok. Can I download it from the App Store while traveling?

My camera is done for and it’s an old phone anyway. From what I’ve read, Tik Tok won’t transfer to my new device. Is that correct?

I’m heading to Mexico on vacation at the end of the week. If I take my new phone with me, would I be able to download Tik Tok from there? Or no since it’s an American iTunes account.