I can't help but feel unpresentable and unapproachable all the time to people around me. I'm friendly with good manners and I'm not ugly; people have told me I'm actually quite pretty, but I feel there is something about me that causes people to judge me instantly before they've even gotten to know me. Like, one time I had to give out questionnaires for academic purposes, and this one girl who I asked (politely) if she wouldn't mind filling one in gave me weird looks. It seems like everything I do turns out to be pointless and meaningless. I'm scared I'll wind up all by myself for the majority of my life and that people regardless of whether they know me or not will hate me. And when I say people, I mean those other than my two good friends I've got, my family and my sister.

Being 'presentable' is good for applying for jobs, not making friends. You are who you are, and they like you or not. Maybe that's a clue of some self-consciousness?
Being approachable is simply a matter of approaching half way. Be nice, be friendly, small compliments about dress or hair or taste in books, and you're now approachable.
Asking people to tell you about themselves or opinions or likes is so much easier and more effective than trying to 'be' something for them.
I'm not so sure people are judging you instantly. Weird looks - goodness, we all get those and more, but it's a matter of brushing it off as nothing. If you want someone to fill out a form and you get a look, just say 'Yes I know, what a pain.' I doubt that the look was aimed at you personally, it's more part of an act about questionnaires. In other words, most of what goes on around us can't be taken personally.
And finally, what do the people you are closest to say about all this? They are the ones who know you. Ask for an opinion, and tell them you can take it. Just listen, don't protest or try to explain. You are looking for help and they are the best ones to give it.