The protagonist of my trilogy-in-progress suffers from a serve case of Borderline Personality Disorder. Among his symptoms are continually splitting, unstable self-image, chronic feelings of emptiness, promiscuity, distrust of others, impulsivity and body dysmorphia (worsened by the fact that he's ashamed by magical markings all over his body and his (TV Tropes link warning!) lacking stature, even though many characters (TV Tropes link warning!) find him attractive in spite of them.

However, one aspect of BPD I'm struggling to portray in believable light is the intense emotional outbursts that the protagonist experiences through the story without him coming across as an inconsistently written character. I fear many readers unfamiliar with BPD's many nuances will simply write off my protagonist as a histrionic arsehole, or that I may get dinged for demonizeing mental illness.

How do I portray the thoughts and feelings of a mood-swing character with BPD in an accurate and sensitive manner?

Thing about BPD is the reactions usually don't come out of nowhere, but are overreacts. I am now going to try to give the most basic example as I can.

Let's say the guy is with someone he loves and feeling all mushy and relaxed because of it. Then this loved one says something in the lines of "Did you forget buying lemons?" A BPD mind goes into a spiral of "What are they implying! Am I that terrible of a human being! I forgot lemons I am so useless! Wait do they think I am useless? They are mad aren't they? It's just lemons I don't deserve this how dare they be mad!" and start yelling. This entire spiral happens in a split second, and that's why you usually don't see him start to fight before he starts yelling like that. So a brief explanation of which nerve it hit - but make sure it's a very brief one so pacing does feel like like it happened in a split second, can be just enough.

But the key is that the spiral is purely emotional - as you can see in my very amateur example, the steps are brief sparks of emotions tying to another, and no pausing to think about what the other person actually said and in which tone. In that split second, due to the rush of all the hormones, the guy with BPD has a very narrow view of things, not properly judging any outside factor.

You could write this particular example as:

Looking at his best friend, moving about to fix this and that, filled Daniel with a sense of peace he didn't expect to feel. Everything was normal once more, and Jack going in and out of kitchen to prepare a meal assured him of the fact.

Jack stared at the contents of the fridge for a second. "Did you forget buying lemons again?"

All that peace evaporated in Daniel's mind. "So what?" he yelled in response, curling his fists. Jack had said again. He was exasperated, wasn't he? Exasperated with Daniel, over fucking lemons, after everything they've been through. "Is that your entire problem? That we don't have enough lemons to stick up your ass?"

Of course, part of it is also that you've already established your character as BPD or at least with its symptoms. If this were the beginning of the book, Daniel's outburst would still look out of place, because we don't know the character and his inner workings, but brief mentions of why Daniel thinks he's right to react the way he does in that moment ("Jack must have been sick of him but over this shit? Really?") will make the reader go "huh."

Now if you ask about how to establish it in the first place to get it to that point, it's just writing tricks. During the getting-to-know-the-character parts in the beginning of the story, have him give reactions like this in situations where pace is slow so you can throughly explain the spiral. Anger and joy tend to be quick and need quick pacing, but you can use longer-winded emotions like sadness or happiness to ease the reader into the concept. For example, the trigger comes in the form of a visual - perhaps a light turning red just when he was about to cross the street. It reminds him of missed chances or being unlucky, and his cheerful mode drops due to remembering these as he thinks about how this is a metaphor for his life (even though it really isn't one). You can extensively explain his being depressed for the next half or couple hours, giving you enough time in narrative to introduce his snappy thought process.

Diagnosis is hard; mirror mood with style

Even with the increased sensibility of our times towards these conditions, I would still have a hard time discerning a person with BPD from a random attention-seeking drama queen. Unless you clearly state that your character has a medical condition, or mention such a possibility at some point, a medically untrained reader like me may completely miss this point.

That being said, there are some stylistic tools that can help you portray the situation. The idea is that the narrator changes both the style and the depiction of the world to reflect the character's mood. You do it subtly, but it will give the reader the unconscious cue that will help relate to the MC. Note that this works for first person POV as well as third person.

My suggestion is to adapt the choice of words to the mood that the character is in at that moment of the narration. If MC is happy, use positive sentences, remark positive elements in the surroundings. If the MC is thoughtful, lengthen your sentences, focus on the inner thoughts of the characters, ignore what happens around then. If MC is angry, use superlatives, short sentences, rough words, a raw and uncouth style.

In this way you will not need to always show what the MC is doing or saying:

(happy) it was a bright and warm morning. Birds were chirping from the magnolia trees. The flowers were a lovely pink vault against the sky, like a fragrant monument to spring. And the bees were bathing in pollen. (Sudden change to angry) The ugly buzzing stingers. Roaming free. Dangerous and unrepentant. MC hated them. Hated their noise. Their look. Their squishy juices.

You portray the mood-swings of a character with BPD believably in the same way that you portray any other emotion of any other character believably –

by motivating the emotions.

The mood-swings of persons with BPD aren't random but triggered by outside events and motivated by internal thoughts, memories, needs, fears, and so on. For example, when a person with BPD reacts to their loved one wanting to go to a party with a dramatic outburst of jealousy, hatred, and self-degradation, this is caused by that person's fear of loss, ambivalence towards their loved one, and their low self-esteem.

How exactly the internal process works in your character is something you will have to make up (depending on the needs of your story) or research (looking at case studies in psychological publications) and write in whatever way fits your narrative style and target audience.