This is okay I suppose; if you're not comfortable with people then this is for you! if you don't feel lonely about it that's good. The big difference is between 'alone' and 'lonely' where 'lonely' is this saddening, gripping feeling of not having anyone who really cares. At least that's it for me.

My mother may be similar to what you describe: I asked her when I was young if she had any friends she could share everything with. She said 'no'. Because that was not how she was: she didn't feel the need to share. She enjoys, or should I say 'enjoyed' (this now makes me sad) to be with groups of friends who had something in common; they would go to a museum or get lunch, all together. Most of them are now gone though.