Thanks for the additional information. It is helpful.
Coughs can occur for a large number of reasons. They can develop upper respiratory illnesses such as kennel cough and canine influenza as well as bronchitis and inhaled allergies. I don't think those are the problem but I want to touch on these. You can read about bronchitis here:
If you are seeing any nasal congestion and sneezing then she may have developed an allergic reaction to an inhaled substance. If this is the case, Benadryl can be given to your dog, the dose is up to 2mg per pound every 8 hours. You likely know this if she has allergies already.
You can read about these here.
Kennel cough is normally contracted when a dog has been boarded or kenneled or around a large number of dogs such as at a dog show, dog park or pet store. Here is a website with more information on kennel cough. http://www.peteducation.com/article.cfm?c=2+2096&aid=452
Canine influenza is now becoming more prevalent and like it sounds it is a canine flu. Here is an excellent site on it.
You will want to monitor your dogs condition looking for colored discharge from the nose or eyes, a productive cough (coughs stuff up), stops eating or lethargy. These are signs of a possible bacterial infection as well and my require antibiotics. If your dog appears to be having a difficult time breathing, you will need to see your Vet as some dogs dog get really sick with canine influenza and need support to recover.
There are other reasons for coughs such as heart problems which should be investigated if your dog is not on heartworm preventative or is an older dog. Since she does tire easily and it is happening when she lays down and pressure is on the chest area, I think the heart is a likely culprit. If it is congestive heart failure a fluid reducing medication might help with the cough. The following site goes over canine coughs.
To help your dog breathe easier you can run a NON-medicated humidifier in the room your dog is in, or sit in a steamed up bathroom with your dog to help keep the mucous moving if you do suspect an upper respiratory illness. Robitussin DM at a 1/4 teaspoon per 5 pounds can be used to control the cough. It should only contain dextromethorphan and Guaifenisen. and should NOT contain pseudoephedrine. it can be used with a heart issue but the condition should be diagnosed first and then your vet can determine if it is necessary and what interactions might be with any medication she prescribes for the heart issue. Dosages can be obtained at this website. http://www.petplace.com/article/drug-library/library/over-the-counter/dextromethorphan-robitussin-dm
Collapsing tracheas often et worse with age as well and often the position of the neck when laying down might lead to collapse.
http://vetsurgerycentral.com/tracheal_collapse.htm I'd go ahead and get her in again for testing to see if she is starting with congestive heart failure. Read about it here:http://www.vcahospitals.com/main/pet-health-information/article/animal-health/congestive-heart-failure-in-dogs/770 I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.