Whenever an 83 year old is experiencing difficulty breathing, she should seek direct medical attention. With a history of both lung and heart problems, this is even more important. A physician has to determine the extent of the problem and treat it before it becomes a real emergency. As you can see this service cannot respond immediately to your questions. I hope you have sought medical care already, but if not, please do so if her symptoms remain. Best of luck.
My mother is also 83 years old but doesn't have as many risk factors. She can also be stubborn but apparently not as stubborn as your mother :-).
Remember that mortality from pneumonia in the elderly is high. Community acquired pneumonia has a mortality of at least 20% after age 50. Being in the hospital has its own problems because of exposure to resistant bacteria, etc.
That being said, if she can't breathe, then she is in a life-threatening situation and you may have to drag her to the ER with the life squad.
My mother had a sinus infection in January that really knocked her for a loop. She began acting really weird. The doctor put her on amoxicillin because I'm sure he was trying to save her the expense of Z-pak (azithromycin). However, after three days she was just getting worse. I called the office, and "suggested" that the drug wasn't working. They prescribed Z-pak and she finally started getting better about three days later. Many respiratory organisms are now resistant to amoxicillin, especially those that cause sinus infections. I work in a microbiology lab and know this from my work. It took her a month to feel better.
You have to monitor the elderly closely, as they will convince you that they're fine when they're really not, and they'll fib about their conditions because they don't want you to go to the trouble of doing things. I found that I had to take the wheel with the treatment options as she just wasn't capable. Her solution was just to say the heck with it all and go to bed. She's an insulin dependent diabetic. She decided one morning not to eat or take her insulin and just go back to bed. Her sugar is usually under good control, and I was shocked when I went over there to find that she hadn't eaten. I dragged her out of bed and got her to test her glucose, which had shot up over the 200 level. It was really difficult to get her to eat or drink when she was sick. She lost about 7 pounds. She's much better now, so I'm crossing my fingers that things stay this way for now. My sister's family all had the flu, and their house is just a pool of infection, as there are little kids and adults all coughing and wheezing. She wanted to go over there to deliver something for Valentine's Day and I put my foot down and said NO - absolutely not. I am the one that takes care of her needs and I couldn't see any reason to expose her to all that illness. If she had gotten what they had it could have killed her, literally.
Good luck with your mom.
http://www.emedicinehealth.com/articles/17666-4.asp
Here is a link saying "when to go to the hospital." Maybe this will help.