While pregnant with my son I also had an irregular heartbeat. Turns out I had a heart murmur. The doc said its harmless and nothing to worry about. It can happen due to the extra volume of blood in our bodies during pregnancy.
Breathing problems can be totally normal in late pregnancy because your placenta has grown so much its pressing on all of your insides, including your lungs/diaghram. But if youre concerned about it, definitely call your doctor or L&D