Hello, Increased heart rate and shortness of breathing is common phenomenon occurring after exercise due to autonomic nervous system activity and inadequate exchange of oxygen and carbon dioxide. Both problem normally settle down after few minute of rest but in few cases it might be due to heart problem like- conduction disorder, arrhythmia , high blood pressure and lung problem like- URTI, pneumonia, pleural effusion, COPD. So you should go for some investigations like- Chest x ray PA view, Echocardiography, ECG, lung function test. Consult a cardiologist for further evaluation. Take care bye.