Take the temperature. Over 102 is a fever (101 in pot bellied)
Pneumonia is certainly a possibility for coughing in young pigs. It can be caused by a number of bacteria. Most antibiotics can be used to treat the bacteria that cause the disease.
Another cause of coughing is parasites particularly roundworm (Ascaris) and lungworm (Metastrongylus). Fenbendazole (Safe Guard) or ivermectin (Ivomec, many brands), are good dewormers for both parasites. The horse past ivermectin can be used. Twice the weight on the syringe is used eg. a 100 lb pig gets a 200 lb dose of horse paste.
Antibiotics and wormers are available OTC in most livestock stores in most states. Amoxicillin and Clavamox are commonly used in dogs. What antibiotics do you have (name and dose).
In addition, let me know if you have follow up questions.
The 250 mg Clavamox would be OK for a 20 pound pig, but is too high for 10-15 pounds. These tablets can not be split. They are not scored and the drug is not evenly distributed throughout the tablet. Tablets lose potency rapidly within hours once removed from the foil wrapper.
The dose for amoxicillin in pigs is similar to other species (10 mg/lb/day). Your pig would get 100 mg for each 10 body weight. You will need to open the capsule and divide it into 5 portions as close to evenly as possible.
Weigh you pig and give it 1/5 of the capsule contents for every 10 pounds of weight.
You can see if the product is soluble in water. If so, you can dissolve a capsule in 5 ml of water (1 teaspoon) and use 1 ml per 10 pounds per day. A 7 day treatment is usually sufficient to treat respiratory infections. Use a syringe to squirt the dose in her mouth.
You can give Amoxi with food. If diarrhea occurs or as a preventative, give her a tablespoon of yogurt with active cultures once a day while using antibiotics.
Deworming every 4 weeks for 2-3 doses should be started if you are not currently doing it.
Temperature is taken rectally.