I'm trying to write a character who is shy and awkward and has anxiety so she would stutter or have social blunders etc. but I'm trying to figure out if the way I write her will end up making her like Bella Swan, a disliked character who has the personality of a tree and people find it hard to believe she has friends or love interests. Basically, I'm trying to get my readers to still actually like and relate to this character without the Bella Swan syndrome. Any takers on this? Thanks in advance.
Disclaimer. I have not read Twilight and have no desire to. However, I'm familiar enough with the character archetype to answer the question.
To write a relatable character you must first utterly convince the reader said character is a living, breathing person who existed/exists/will exist in a specific time and place.
Nothing less will do. The plot will (hopefully) chuck many sharp objects at your protagonist as she moves towards her goal. When she's hit and starts bleeding, I want to watch her clutch the wound, curse loudly, pick herself up and keep moving. If instead the knife slits a hole in her sweater and a bunch of packing peanuts fall out, revealing the MC to be a mannequin mounted on a RC car, I will close the book and stop caring.
What makes a character feel human, then? That's an awfully large question and open for debate, but you already hint at one important aspect: the presence of flaws. Hotheadedness, cowardice, a martyr complex -- packing peanut-stuffed mannequins don't have these negative qualities. They're uniquely human.
Here's where I think a lot of people will disagree with me (especially writers for teen TV shows), but anxiety and social awkwardness are not character flaws. Anxiety is an emotion anyone can experience; awkwardness is one mechanism by which the emotion shows. You can stick these 'flaws' on a character like a pair of googly eyes, but they're instantly recognizable as fake.
That's not to say you can't write a socially awkward character. However, you should consider what happened earlier in the character's life leading her to develop a flaw that causes her to screw up in social situations. Perhaps her parents moved a lot and she never had friends for longer than a few months, eventually causing her to believe the effort isn't worth it? I don't know, you doubtlessly have better ideas.
In short, before or while writing, figure out why your character is who she is. If you don't buy the explanation, neither will the reader.
The answers above are pretty good already so I'm just adding a few extra bits. Basically, you are approaching the problem from the wrong angle: the question shouldn't be "How do I make my socially awkward character likable", but "How I make my likable character deal with a crippling behavior", if that makes any sense. One thing that could help you is to write down the background of this character, starting with what makes it a likable person, then expending to her full background. You don't need to include all this background in your story, but it help you predict how your character will react to situations.
Shy or introvert people are like everybody else: they have hopes, dreams, qualities and flaws. Maybe she's very shy but extremely funny when we get to know her, or maybe she's super insightful. Maybe she's truly passionate about something, or have a special talent that only waits to be noticed by the people around her. Get to know your character: what does she likes, what are her hobbies, her favorite things to do? How does she likes to dress? Does she have friends or a role model? Where does she likes to hang out? What are her flaws, what gets her angry? What could pushes her to make the wrong calls? What situations causes her to stutter? Borrow traits from real people you got to like if that helps.
Once you know what kind of person your character is, you'll be able to write believable situation where she would act awkwardly and still get your reader to root for her. And remember: if that character is important to your story, there should be at least an obstacle to overcome that help her triumph over her flaws (or at least mitigate them): having to make a big speech, asking the popular guy out, whatever suits your story. You read a story to get a sense of progression: if your character is as crippled at the end of the story than it was at the beginning, there's not much of a point in reading about her. Hope it helps.
Making a socially anxious character is very simple in design. I myself am quite socially awkward at times. But I also enjoy engaging in social activities, have quite a few hobbies, and can speak very well when I need to.
Now, Twilight, from what little I read, is very much fanfiction-esque. It features a bland protagonist that is supposed to fill in for the reader to be able to assimilate themselves into, a love interest that is pretty much perfect (to the author) and is basically wish-fulfillment in a book. One very common flaw people have is social awkwardness. It's easy to identify with because we've all been there.
As an avid reader and budding author myself, social awkwardness is a flaw we all suffer for to some degree. What you 're really looking to do is make you character believable in another way. I personally like to have awkward moments for all my characters, so I try to develop my characters in other ways, like giving them anger issues, or having them be the overprotective mother, etc.
So, what I think you should do is observe people in awkward situations (romcoms are gold for this type of stuff.) and see how they react. That, although exaggerated, is very human and can be used for development.
It's not really social awkwardness that you should be looking into, it's the other things that make them human. Hope this helps, and isn't just me rambling.