Yes, there is a female version of blue balls and I have it right now. 
First of all, let me explain what “blue balls” is.
When a male is horny, blood rushes to his genitals and *poof!* an erection! If arousal goes on for an extended period of time without ejaculation, this causes vasocongestion. Vasocongestion is the accumulation of blood in the blood vessels of a region of the body, especially the genitals. This causes his balls to swell (normal swelling during erection is 20% but can increase over extended periods of arousal), become sore, and possibly take on a blue tint.
Female Blue Balls, or Blue Vulva
Just like men, women have a surge of blood towards their genitals when they are aroused. When aroused, the labia, vagina, and clitoris swell and lubricate. So, women are more likely to feel this soreness in the labia, clitoris, and the outer third of the vagina. There’s also the possibility of the vulva darkening due to the presence of extra blood.
This is what I’ve been dealing with. My labia feel so swollen and sore right now. I’ve been pretty frisky since yesterday evening after sucking hubby off, and I still haven’t gotten anything myself. Although he knows I’m frisky, he keeps brushing me off just to drive me nuts. Yes, I could try to take care of myself, but he’d probably catch me, stop me, and make things worse by getting me even more sore. 
The Remedy
Plain and simple, to fix blue balls or blue vulva, you need an orgasm. After orgasm the body can return to a relaxed, non-excited state. Tension is released by the pulsations of muscles coming to orgasm or expelling ejaculate, and arteries and veins return to their normal size and functioning as blood quickly drains from the genitals, relieving pressure and reducing their usual size.
No orgasms means no relief. Both genders can experience a feeling of aching or heaviness in the genital and pelvic areas, because of vasocongestion. It’s very uncomfortable, but it’s not damaging to your health. There are other remedies for blue balls/blue vulva. These include application of an ice pack or warm compress to the genitals, or a cold shower. I always wondered why guys take cold showers. Really, I’d rather masturbate or have intercourse, but I guess when that’s your only option… 
The worst is when I get a dirty text when I'm stuck in traffic - I get the WORST blue vulva!! Torture ;)
I honestly don't think I've ever experienced this and don't think I really want to. Hope things get better soon.
I knew girls could also have something similar to blue balls which I just though it was a really bad case of "I need to get it on now or I am going to go crazy" I mean how could girls not get as hot and bothered as guys. I called it pink ovaries until you let me know it was called blue vulva. Once you told me I felt like I was not an extremely horny girl. That if their was a legit name for it, it was cause others were experiencing the same thing.
Lady Estrogen,
It most definitely is torture!
Nanny,
Thanks, but it usually never lasts too long. It's all hubby's fault, though. :p lol
Angel,
Yeah, a lot of girl get blue vulva, unfortunately.
It's agony - torture - and the worst thing is that sometimes it's so bad that 'getting off' won't happen until relaxation occurs and this is dizzying.
I hear you - I get it - frequently the only thing that helps is a hot bath and fun with shower massage, then head for the nightstand or hubby and it's really sometimes so bad I'd rather he just let me get it over with before we can have fun.
Unfortunately, most of the times that I get it are when I'm out and about. Walking with female blue balls is REALLY uncomfortable...
A hot bath with a shower massage sounds like it would definitely help. My tub has those stupid non-slip stickers in it, and we have no detachable shower head, though. Hopefully, that will be remedied soon.