Her weakness/lethargy are likely due to low blood glucose, dehydration and an imbalance in blood electrolyte and mineral balances that all go along with a dog that is eating so poorly they are losing weight and breaking down their body for energy to support basic metabolic functions.
A change in breathing may indicate lung disease (infection, granulomas, or masses), or metabolic acid/bases imbalances that the body tries to clear via exhaling waste products.
In many cases loss of appetite is triggered by eating something they should not, too much table food, too many treats or something they find outdoors, or a dietary allergy or sensitivity.
More serious/chronic causes that lead to weight loss include chronic viral or bacterial infections, chronic pancreatitis, inflammatory bowel disease, internal organ failure (kidney or liver disease, ketoacidotic diabetes), a full or partial gastrointestinal obstruction, an abdominal mass putting pressure on her gastrointestinal tract, or even infiltrative cancers such as lymphoma.
Dogs won't purposely starve themselves, so because she is losing weight that indicates a significant, chronic disease and an examination and some testing is needed as soon as possible.
I would recommend an examination, complete blood count, biochemistry profile and urinalysis. In many cases this can point toward a diagnosis and direct treatment. But with many cancers bloodwork and routine radiographs may not be diagnostic. In those cases an abdominal ultrasound can be helpful.
In the meantime at home to try to settle her stomach and get herr to eat you can give an over the counter acid reducer that people take for acid reflux, either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 15 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 30 to 80 pounds of body weight every 12-24 hours.
These are acid reducers, are very safe, and may help her feel better. They can be used as needed.
I understand she isn't eating well now so getting medication in would be hard. You can pop the pill down her throat, or crush the pill, mix with a little water or clear broth and use a medicine dropper or syringe (needle off) to squirt it into the back of her mouth.
If she isn't cooperating hold her muzzle closed and tilt her head up very slightly with one hand. With the other hand guide the tip end of the medicine syringe in her mouth on the side of her mouth where the upper and lower lips meet, placing the tip between her premolar tooth crowns and squirt it in. Then gently rub her throat as you continue to hold her head up slightly. She should be forced to swallow it that way.
You can also try a bland diet with increased fluids to perk her appetite and get her better hydrated. A homemade diet for this is 1/3 boiled, lean hamburger or boiled, white, skinless chicken, all fats and juices drained off the meat, and 2/3 boiled, plain white rice. Add low salt beef or chicken broth to her meals as well to improve palatability and get more fluids in which should help as well.
In an older pup with these sorts of symptoms it is likely she has some sort of serious disease process going on if she doesn't respond to simple supportive care. She needs diagnostic testing to further evaluate her.
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