Hi MM! Hours of coddling? No way!
I have boys. They are certainly more rough and tumble. But I think that perhaps you might want to treat her more like a boy with this.
I would treat her wound, tell her "That's enough, Susie. I don't want to hear anymore fussing about this" and then walk away from her and go about your business. If she can't calm herself down, send her to her room.
Do you have have hair detangler? I'd spray her hair with that or cut it short. If she balks over having short hair, tell her that when she can stop screaming about combing her hair, she can grow it long again. That might be a while.
I wouldn't let her continue her tirades for days on end. For bug bites, putting on the hydrocortisone several times a day is fine - those bites can get infected if she scratches them. But other than a bandaid, I'd tell her to hush up after the initial onslaught.
The only thing that I will suggest that is NOT part of the drama queen spectrum is the possibility of a sensory problem. My younger son had the OPPOSITE problem - he didn't feel ENOUGH, so he was forever crashing himself into stuff in order TO feel. Sensory disorders present in a lot of different ways, including being TOO sensitive to touch. That might include pain. You could talk to an occupational therapist who works specifically with sensory issues and ask about helping with your daughter. Maybe that would make a difference, in tandem with you not allowing her to "perform" in front of anyone.
Good luck!
Dawn