Pulling an idea out of Rae, and a certain Fiasco game in which an alien STD played a huge part in the game, there's totally a Monsterhearts skin or a set of moves that one could build out of a supernatural STD.
This is a skin about a person who's body disgusts them, about self-image, about being shamed by others, about dying young and all the things that go with dying young. There are all sorts of feelings of shame, self-disgust, and feeling horribly rejected and unloved. Inflicting harm to others, and feeling guilt for it.
Other people must have an incentive to sleep with them. I mean, they're probably super desirable (this is Monsterhearts, after all), but the character's sex move probably offers a huge incentive to sleep with them. The player character also needs incentives to not tell people what's happening with them right away - so they don't discover until it's too late.
The disease could be a lot of things, this is probably the Origin, and suggests where the illness is going: A curse, a demonic plague, you're becoming something else, you have something living inside of you.
It might be wise to have some origins point at other skins, in case the disease progresses and the character dies. So, if you have a zombie-kinda illness, you return as a ghoul. If something is living inside of you, maybe you are giving life to a dark power as an infernal, or shedding your flesh and becoming a (probably dark-tinged) fae. Whatever makes sense for the game.
Spitballing:
Sex Move: The you have sex with someone, the illness spreads. They gain the condition diseased. If they did not already have this condition, they gain a string on you, and they mark experience. Or maybe you both mark experience. And maybe your character heals a Harm, too.
Darkest Self: Nobody is ever going to remember you as anything other than a diseased wretch. They'll be happy when you're gone. Well, if you're going to go, you're going to make sure they all feel what you're feeling, and they'll all follow in your footsteps.
Ashes, Ashes: Whatever you roll, on a 6-9 you may add "Take a harm, and mark experience" to the possible list of outcomes.
Ring Around the Rosie: You probably gain a benefit when interacting with someone who has the condition diseased, too.
We All Fall Down: Maybe people take harm when they are diseased, and hit a certain condition. Possibly when they roll 6-9, or someone rolls that against them.
Shameful Secret: Any time someone, yourself or another person, keeps your condition a secret, that person marks experience.
Highly Infectious: Add "Give or get the condition diseased" to the 6-9 list for Lashing Out Physically for all participants in the scene.
Feel free to contribute.
Edit: With a more generic skin name, and maybe the option of another name for the condition, this could also be kinda Final Destination or Drag Me To Hell-esque (or the way Rae seems to be working out). In this instance, any harm you take through Ashes, Ashes represents an unlikely injury or coincidences. Someone you're shutting down shoves you to punctuate a point, and accidentally knocks you down a set of stairs. While lashing out, a gun you're shooting backfires or ricochets, and you hurt yourself.
All of the skins have more than one way you can read it, so this idea might be a thing needed to round out this skin idea. Accursed might be a more generic name.