No, I haven't moved to a different country and I haven't hidden my music.
I checked iTunes on my computer for my purchased items (Account > Purchased), but for some reason it says I don't have any purchased music available to download? Though I'm not sure if it says that because my computer already has all my purchased albums downloaded into its iTunes library. So the issue is that the songs are present in my iTunes library and in my old iPhone, but for some reason, they don't show up in my list of Purchased songs in the iTunes Store app on my new iPhone or on my computer (assuming that, regardless of whether or not my computer already has them downloaded, they should still show up there), which is preventing me from downloading them.
EDIT: Huh, never mind what I said. For some reason, they were hidden after all? I don't understand how that could have happened. At any rate, thanks. I think this solved my issue.
EDIT2: Yeah, I restarted my phone and was able to redownload the missing songs into my new iPhone. Though now, one of the albums has been separated into two for some reason. I'm not sure if that's because they were downloaded separately or if iTunes updated to separate them like that for future downloads since the second half of the album contains music videos instead of just songs and they were just put together into one album back when I first purchased them.
One album is still missing, though. Unsure of what I can do to redownload it since it wasn't hidden like the other two albums that I was able to redownload. If it's relevant, it's put under a "Compilations" header (though one of the other albums was also put under Compilations and I was still able to unhide and redownload it).