This prompt is definitely on the spooky side. It’s not something that could happen in real life unless a very large group of people conspired to convince two people they were crazy like this. I would say I can’t imagine what would make people do that, but I actually probably could imagine what would make people do that. I have a pretty decent sized imagination.
That’s not what I want to focus on here, though you are welcome to do so. I want to go at this idea as if something supernatural is going on. The first thing that comes to mind is that when the point of view character returned from their vacation they entered some sort of pocket dimension with a skewed version of reality.
The point of view character noticed the lack of their best friend, because their best friend was important to them, but maybe there were other people missing, too. The best friend, on the other hand, was in normal time and space and for some reason remembered their best friend. Maybe it has to do with how close they are or maybe they did something when they were younger that linked them together so that they cannot forget each other.
So what happens next? Everyone is convinced that they are both insane. I’m not really sure how the point of view character ends up in the asylum without the people who bring him or her there knowing unless maybe the people who brought them there was the one who sent them into the pocket dimension in the first place.
The character is brought to the asylum and finds their friend there. Based off the wording, I think the friend was their first. Maybe this goes with the idea that someone was messing with them, someone who wanted them to suffer a bit first, someone who probably knew exactly what was going on with the best friend.
After they find each other and know the other is alright, they are still in an insane asylum. Maybe they try to get out. It could be difficult to get out without someone outside saying they were allowed to leave. The trip to the asylum might be considered temporary with the plan being to remove them, or at least the best friend, once they are doing better. Or is the plan for them to stay there with the assumption that there is no way to come back from this? This one seems a bit more difficult figure out unless we go back to the idea of a massive conspiracy to trick them, but maybe you have a better idea how to handle it.