Welcome..How old is this girl & how long have you had her??
It could be severe gingivitis (inflammation of the gums) or maybe she has lost a tooth? She also may have bitten her tongue, or possibly she has some lesion in her mouth which needs vet's attention.
I knew a dog once who bit his tongue, and the blood just flowed out! He was okay once it healed, but it was very scary when it happened.
Take her to a vet to get her checked.
Teeth and gum problems (plaque) are often a problem in dogs in the USA that have been taken in by a shelter. In my experience here in the USA the "public/government" shelters generally do not provide any veterinarian care beyond putting the animal "down" if it is in pain or not adoptable. Private shelters are normally "no kill" and do provide a lot into putting all dogs they put up for adoption into a good health state..this depends of course on funds...but I think most have some sympathetic veterinarian care at below "advertised prices"...don't really know.
I provide the about first as tip on what the problem may be, and to let you understand why we would suggest taking your dog back to the shelter to see if they can provide some help, or at least an expert opinion on what is needed.
Good luck, please let us know what you learn
She should be checked out by a Veterinarian. We have a ShihTzu, too, and have never had anything like that happen. If you can't get an appointment with your Vet, then please take her to the shelter where you adopted her to see if they have a Vet on call to ascertain her condition.
Please stop back and let us know how she's doing.
Cheryl
MH Community Mgr