Any tips on how to write someone with mild anxiety or social anxiety?

Instead of insulting you, I’m gonna give actual writing tips lol. 

There’s many different ways to go about showing anxiety. First idea: I’d suggest showing the character’s anxiety without saying they have anxiety. Ex: saying her palms were sticky with sweat instead of saying she was nervous. Don’t say what emotion the character’s feeling, show it. 

Another strategy would be to give lots of internal dialogue. Many people with social anxiety have racing thoughts and concern over situations. These thoughts are italicized. To take it a step further, you could compare what the character is thinking of the situation to how a bystander is viewing it. A lot of the times, anxiety can result in weird or awkward behavior, or cause the person to view the situation out of its proportion. So, you could compare the internal fear and dread of the anxious person with the mundane reality of a situation that’s just “no big deal” to the average person. Hope this helps.

(Edit) Adding on top of the second strategy, a socially anxious character could be considered an “unreliable narrator”. This means that the reader’s view is warped because the narrator is heavily bias or unrealistic. Other examples of unreliable narrators would be schizophrenic people or other mentally ill people who see the world differently than the average person. This would have to make the anxiety more extreme and very character focused (completely inside the head of the narrator) but could make for a very interesting story.

I used to be very socially anxious, so I can confirm the sweaty palms, wild thoughts, racing heart, etc. One thing that might inform the character's actions is avoidant behaviour - people with anxiety often avoid the situations that they believe will make them anxious. This could be anything from wearing headphones to deter strangers striking up conversation, to preferring self-checkouts over people at the till, to always being late to meet-ups to avoid being the first one there and having to wait alone.

Anxiety creates a loop of 1) fearing an event, 2) avoiding that event, and then 3) because the worry about the event is never disproven, 4) the brain keeps believing it to be true, and 5) keeps fearing it. It's a subconscious loop that the individual reinforces without realising in order to avoid feeling fearful, because it's often upsetting and exhausting. This might give you some insight into the character's thought process at times. 

I believe there are videos on YouTube in the genre of 'A Day In The Life of an Anxious Person' if that might help with your research. Best of luck with your story, I'm sure it'll turn out wonderfully! :)

Lots of fretful internal thoughts and stream of consciousness. Lots of questioning, especially using the phrase “ -what if? “

Lots of over-analysing and over-thinking. 

Lots of contemplating what to say before they say it. 

Procrastination and prevaricating before doing. 

Waking up with knot-in-the-stomach feelings. 

Things giving them dopamine hits (ie click bait headlines) 

You mean how to create the character for this type of person in your writing project, correct?  On the surface, it seems as if you are asking how to address a letter to someone with social anxiety, a.k.a., a "worry wart."  Review the show "Monk" that is still being shown on cable TV, and get a feel for the neuroses with which this well-developed character deals while solving cases.  Also review all of the people you've known who fear taking risks and jot down (free associate) some of the traits that stand out the most.  Are you ever plagued by "mild anxiety" or "social anxiety"?  If yes, start an introspective journal that analyzes your own angst, then compare this with the other examples.  

One phrase I like to use for people who put blocks up for taking action is "a case of the 'yeah buts.'  For example, if someone tells you they have a headache and you offer an aspirin that the person refuses by saying, "Yeah, but...what if the aspirin upsets my stomach" or some such rationalization, then you can reasonably assume the person wants to have the headache.  You could at that point say, "Are you bragging or complaining?" if the person continues to complain about having a headache.  

My guess as a 75-year-old poet and writer is that you already know deep down what you want to say, but you are putting up blockades for yourself to avoid making a commitment, journalistically speaking.  Just put your pen to a blank sheet of paper and build up what a professor I know called a "word horde"---write down one word on that blank sheet, then focus on your goal (defining a person with anxiety) and put down any word that floods into your mind.  Put a mark (like an asterisk) next to any word that strikes a chord, but keep going until a pattern starts to shape itself.  This exercise should awaken all sorts of inspiration.  

You need to do a lot of real research on the subject. That's what writers do.

Besides the research, think of what an anxious person or a shy person might think, feel or do in the situation you put them in.

Were you not anxious the first time you drove a car, or prepared for a surgical operation or wrote an important examination?

Were you shy the first day in a new school or a new job? What about meeting a person important to you? A crush? What about if you were overdressed or too casually dressed that you stood out like a bloody corpse at a bridal shower?

Sure thing, Randi (Randi!!!). You just get a pen - or a pencil, of course - and write "someone with mild anxiety or social anxiety" on a bit of paper. Hell, you could write it anywhere, really. On the wall, say. Or the road. Or the side of a car. In which case you'd probably want to use paint, or something. Hope this helped with your badly-researched question. Yes.

Nobody ever wrote a worthwhile book from "tips".

Go and do some solid reading. And then do what real writers do: use your IMAGINATION and empathy.

I second Cogito's reply. This is why teachers urge students to write what they know, to lessen the amount of necessary research.

It's also important to consider whether the person with social anxiety disorder is the point of view character or someone who is merely observed by the POV character. What the SAD person feels and thinks is not the same as what they show.

My SAD child was often thought to be stuck-up, for example.

You need to do a lot of real research on the subject.  That's what writers do.  Expecting good advice from a few random strangers on a website isn't nearly enough.