Often I have tachycardia, chest pains and sigh a lot. Is sighing connected to the palpitations?

Can be. The tachycardia could contribute to chest pains. The sighing could be due to your breathing trying to up its ventilation rate during the attack. Have you had a doctor check you out and run tests.
Yes. When you breathe in (inspiration) your heart rate increases, physiological, especially notable in young individuals. The other symptoms of chest pains and sighing a lot may be due to anxiety, you need to see your doctor for reassurance about your heart condition, and counseling about anxiety, best wishes.