I've just been through a battery of tests for recurring heart palpitations: ECG, three day R test, calcium score, exercise echocardiogram stress test. No heart disease found. Everything normal
They aren't painful, they just feel like a gerbil flipping out in the chest for a few seconds. They tend to come on about forty minutes into a ride, and then recur each time I exert myself. They can feel like trapped wind that needs to be burped out.
Docs say they're nothing to worry about. But I do find them disconcerting and can lead to anxiety (which may explain your tight chest feeling, but I am not a doctor) and I do tend to slow my ride pace if they happen.
If they keep happening, see your GP.