Two main things affect you when you are alone;
1. Identity and personality - A lot of how you see yourself is in comparison with other people. You might describe someone as boring, or angry, or stupid, but these labels only apply in the context of "other people". Some sort of social average you have in your mind. Some guy who goes around punching people may seem aggressive in most middle-class western cultures but might be considered mild in some tribal warrior village.
Without the usual cues of social context your behaviour loses it's compass. Lots of people (younger generally) gauge how happy or comfortable they are based on how the feeling, right at that moment, about the people around them. Take that away and many are not sure if they're supposed to feel happy or sad. Also you lack a certain amount of mental stimulation. Your brain starts to "eat it's own thoughts" as my mum called it and that's usually not a good outcome if you're trying to figure something out but not getting any new information.
2. Environmental Cues - Despite people thinking they're are free-willed, self-destined creatures (they are essentially), a lot of your behaviour is determined by your environment, what's around you. You don't behave the same way at a restaurant as you do at a sporting event. You don't talk to your girlfiend/boyfriend the same way you do to your parents. In the absence of people a lot of environmental cues you're used to, that you rely on, are now missing. If someone usually makes your evening meal for you, you suddenly find you eat different hours. If you go to sleep at a different time it's probably because you judge when to go to sleep based on someone else's behaviour.
For example, just say you go to bed when someone else starts watching a late show. If their behaviour isn't there as a cue, then your behaviour will probably change.
But to the OP. As far has having depressive and nihilistic thoughts (apocalyptic fantasies and such), it's much more likely you have some unresolved issues, and let's face it, who doesn't. But it sounds to me like you're not comfortable with your view of the world. Personally I always find this feeling when something I believe in, a faith and I don't mean a religious one, conflicts with how things really seem to be. For example, I want to see people as fair-minded, generally good people. But what I see in them is frustration and anger. I see people exploit any weakness they can find in others and attempt to put themselves above that person. I can't have both the belief and the evidence in the same head. Or it might be that I want see myself as interesting and well-liked but a lot of people seem disinterested when I talk to them. Generally this requires self-analysis and eventually a revelation where I find a way to resolve the schism.
However, these schisms can be anything. Maybe for you it's the conflict between feeling confident and self-sufficient yet feeling scared and anxious when you're alone. It may be some other aspect of your life manifesting itself.
The comfort I can offer though; 1. It's common, very, very common. People are social creatures and it feels inherently "wrong" to be alone for most people, which leads to anxiety. 2. Apocalyptic fantasies are pretty common in young people, especially young men. There's a lot of waffling wank around why but the one I think fits is that at that age you are struggling to determine your identity. What do you see yourself as (see the Erik Erikson's stages of development). Up until now your role in the world has largely been defined for you by school, friends, parents, etc. Most of this is out of your hands. And generally you have to play many parts to many different people. When you get out of that you're suddenly in the abyss where you have to figure it out for yourself.
That's scary, particularly if you have the fear that you may not like who you really are. The only way to figure it out is to go experience life. Only when you can see how you feel and react and choose to behave will you begin too see who you are. You need to test yourself, experiment and the results will give you the evidence you need to say "This is who I am. I know this because....". So the apocalypse represents the death of the world as you know and a clean slate to start. I'm assuming your fantasies about it typically involve "What would I do in this situation, what would I do about that" You're basically casting out all the enforced social conventions and rules you've been forced to follow, allowing yourself the freedom to think about how you actually feel about what's right and wrong and what people should do. It's a healthy process so don't guilt yourself.
You could also go the route of distraction. Playing games, watching movies, etc. There's nothing wrong with that. In fact it's a good thing if what you're doing is expanding your mind in some way. And by that I'm not suggesting it has to be some philosophical epic book. It could be playing Halo and setting yourself the goal of figuring out where all the weapons spawns are. Just as long as it's something you're "learning" your brain will appreciate it.
Hope this perks you up a bit. Believe me when I say life gets easier, at least in the terms of these kinds of problems.
