I'm with Dale. Try it you'll probably love it. I have done about %85 of my trips solo. For some reason most of my immediate friends at this moment in time are the type that look at me like I am insane when I describe how fun it is to be out there. When going in some more potentially dicey and remote territory I did a few organized Sierra club trips. I think never again. I like it best with one or two simpatico friends, but no more.
I get the part about worrying you will injure yourself and not have a buddy to go for help. But there are ton of places and times of years when you can do nice long solo trips, but are guaranteed to run into people. Try doing a few trips like that first. There are even some places like the JMT where going solo can be quite the social experience. This type of thing can relieve you of some of the bigger "what if" worries initially, while still giving you a taste of real solitude. It is a truism that you can experience much more solitude going solo in a well traveled area than you ever could with one or two companions with you, even in say, "the maze" in Utah.
Then if it isn't for you stop going solo.
As far as the "weirded-out" feeling some people have when being alone without the comforts and security blankets we have in society and constant interaction with other people, I think analyzing and potentially overcoming that fear is one of the reason for going solo in the first place. I still occasionally feel it flicker briefly across my consciousness, but it doesn't bother me any more. I have my own interpretation of what this "is about". It is the intuitive realization that while we can love Nature/the universe or whatever - it does not and cannot love us back.
Or maybe it was just that strange noise you just heard. LOL
Anyway, probably experiencing that as part of your solo adventures, if only briefly, is something as good for the soul occasionally as good times with friends. Both scary, and at the same time freeing.
OK, probably should have posted this in the Existentialist Ramblings sub-forum. :-)
Anyway, just do it!