Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I am very sorry that your girl has a bloody vulvar discharge.
There are many reasons to have blood in the urine or bleeding from vulva.
We often think of an infection but also crystals or stones in the urinary tract, masses in the vagina, or in the urinary or reproductive tract or clotting disorders are possible causes. If she is an unspayed female endometritis or a pyometra are possible causes as well.
Are her gums and tongue white, pale pink or bubble gum pink? If they are nice and pink then she likely hasn't lost enough blood to make her anemic and that is a good sign.
Is she bleeding only when she passes urine or does the bleeding ever seem independent of passing urine?
If the bleeding is only when she passes urine then concerns would be a genitourinary tract infection, crystals or stones in her urinary tract, a clotting abnormality or a mass in her urinary or reproductive tract.
If the bleeding is ever independent of her passing urine the concerns would be trauma to her reproductive tract (rough breeding), a mass in her lower reproductive tract, a pyometra (infected uterus), or a clotting abnormality.
She does need to see her veterinarian. I understand that you are concerned that they may recommend euthanasia but that is your choice, not their's and she feels quite unwell so it isn't fair to let her continue the way that she is.
If she were my patient I'd start with a urinalysis with culture and radiographs of her abdomen to look at her kidneys and bladder for signs of stones and the size and shape of her reproductive tract. We may need an abdominal ultrasound to identify some urinary calculi and masses in her bladder or reproductive tract. If she had pale gums signifying significant blood loss then I would want to check her clotting function too.
If this is a reproductive tract infection I highly recommend that she be spayed, those are not amenable to antibiotic therapy, because the antibiotics cannot fully penetrate.
All you can do for her at home is encourage fluid intake to flush out her urinary tract. Add water or low salt beef or chicken broth to her food or feed her canned food to encourage eating and increase her fluid intake.
Give her ice cubes. Offer her fresh water frequently.
And make sure she gets out frequently to urinate.
If she is straining but unable to pass urine, is vomiting, runs a fever (more than 103F rectally), has a tense, painful abdomen with gentle pressure, or her gums become very pale it is time for emergency veterinary care.
Please let me know if you have any further questions.