Photos I’ve favorited do not show up in the Favories album

I just tried this on my iPad where "Download Originals" is checked, and the picture I favorited showed up in Favorites by the time I navigated to it there. I checked my iPhone, synced with my iPad through iCloud, and the favorited picture was there in favorites, as well. By "like a photo" you do mean selecting the little heart icon, right?

So I don't know what's going on. Try a forced re-start to see if that changes anything:

Force restart iPhone - Apple Support

How long have you waited? It may take awhile. Photos will be scanning all the images to determine if anything's changed. I tried it, and I can't find the newly favorited picture in Favorites, but I have 15000 of them, and I'm not sure I looked hard enough.

Are you using iCloud to synchronize your Photos?