Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry that you have been waiting for a response, but your requested expert isn't online which delayed your question coming up on the list for all to answer. I would like to help if you are still interested in an opinion.
A normal small dog has a resting respiratory rate of about 10 to 15 breaths per minute, and one breath is considered the in and out motion of her chest. If she has a rate faster then 40 breaths per minute then she is in trouble.
If you can notice that she is breathing abnormally then I am concerned for her.
Is she eating and drinking normally?
Is she lethargic?
What color are her gums and tongue? They should be a nice bubblegum pink. If they are white or blue gray in color then an emergency clinic visit is best.
You mention that her mouth feels cold. Can you take her temperature? Normal rectal temperature is 100F to 102.5 F. A fever is anything higher than 103F, and if her body temperature is below 99F that is a big concern. Dogs that cannot regulate their body temperature enough to keep themselves warm are critically ill and deserve a visit to the emergency clinic.
If she doesn't have a nasal discharge and isn't sneezing then her difficulty breathing is likely related to a problem in her chest or secondary to anemia (decreased numbers of red blood cells).
Problems in her chest leading to an increased respiratory include primary heart disease (including cardiomyopathy, heart valve disease and heart failure, and heartworm), lung disease including obstructive bronchial disease, bacterial, viral, parasitic (lungworm) or fungal infections, a mass(es) in the chest including lymphoma, heart based tumors or carcinomas, or fluid around the lungs (pleural effusion) due to a mass, bleeding, chylothorax or an infection.
Anemia can be secondary to poor red blood cell production, either due to kidney disease as the kidneys make a hormone to stimulate production or primary bone marrow disease, or anemia can be due to bleeding or destruction of red cells due to a tumor, blood parasite or autoimmune disease (body attacks its own red blood cells and destroys them).
If your girl's tongue and gum color are a nice bubblegum pink them she is in better shape then if her gum and tongue color is blue or gray, these would signify she is real trouble and this is a true emergency.
The conditions I listed above are serious and I would highly recommend that your girl see a veterinarian promptly to have an examination and further testing done based upon her examination.
Emma likely needs radiographs of her chest to evaluate her heart and lungs and basic blood tests to start and then further diagnostics based upon those findings. That may include testing for heartworm and lungworms, aspirating fluid for examination if there is fluid present around her lungs, or blood titers for fungal infections.
In the meantime keep her quiet so she can breathe as easily as possible. Unfortunately there isn't much that you can do at hime other than keep her warm if her body temperature is truly subnormal and syringe in fluids (water or pedialyte) orally to keep her hydrated.
Please let me know if you have any further questions.