Elevated heart rate, shortness of breath and long-term sinus(?) problem?

My mother is almost 78 years old and has been chronically HEALTHY....not the sedentary type AT ALL.

BUT, March 2006 she got a cold and can't seem to fully get rid of it. NOW, she frequently has an elevated pulse, shortness of breath, and, consequently, tires very easily. She is a VERY healthy weight, about 5-5 and 125-130 pounds and takes good care of herself. She has moderately high cholesterol -- 211-ish, I think -- and manages it with her diet. She's had the sinus flushing "surgery", but no improvement. She's not in a dwelling with polybutelene (PB) pipes, so we don't believe there's a mold-causing leak that's causing the sinus problems and chest congestion.
Several Drs., 2 CT scans, and 1 or more xrays later, one Dr noted some calcified scarring in her lungs -- MAYBE from pneumonia -- and suggested early stages of emphesyma. OH, AND, though 2 Drs have noted her elevated pulse, they haven't bothered with any investigation of her heart.
Any ideas???

I would point blank ask the dr to check out her heart....they may be focusing on her shortness of breath because that seems to be a major complaint......some heart dysrhythmias can certainly cause sob......I would ask, sometimes it helps to plant an idea.