No it is perfectly fine. Your heart rate
is expected to increase when you exercise. As long as you are feeling fine, then it is not something to worry about. It suggests your heart is very healthy to be able to sustain that kind of heart rate. A normal maximal heart rate is 220 - your age. The trouble breathing is a little more worrisome. It could be due to a number of reasons including deconditioning, exercise induced asthma
, etc. If you are concerned, see your doctor about this.