It can be lonely, I agree. But some people who are married are lonely too, or have their own running struggles in their partnership. It's easy to feel that the grass is greener. Of course, I don't want to say that the values of intimacy and connection aren't something we should want--of course they can be wonderfully rewarding. But only if they're right. It's far better to keep being self-sufficient and wait to see whether someone comes into your life who will deserve you and be a good partner than to waste your energy now on wishing you had that.
I know it is easier said than done. I can tell you that it's obvious from your post that you would make some man very lucky and happy. For now, making yourself happy is no second choice at all. It doesn't have to mean you are never allowed to wish for companionship however. Just acknowledge that sadness, and try to move on past it and look at the bright side.