Thanks for your question on Health Care Magic.
I can understand your concern.
Yes, coughing can cause
tachycardia (high pulse rate) and fluttering feeling in heart.
Coughing is commonly due to upper or lower
respiratory tract infection.
And tachycardia is common in infection.
Coughing itself causes strain and exertion to the body. So all these cause tachycardia.
So better to
consult doctor and get done clinical examination of respiratory system and chest
x ray to rule out lower respiratory tract infection (LRTI).
You need antibiotics, antihistamines and anti inflammatory drugs.
Drink plenty of fluids orally.
Avoid
stress and tension, be relax and calm.
Don't worry, you will be alright.
Hope I have solved your query.
Wish you good health. Thanks.