How to say this in English: after running a long distance or excercise,my breath is very fast ..(is there any one word or one sentence for this ?)

If I'm understanding the question correctly, I would call this being "out of breath" or "winded." We often use this term to describe being out of breath after exercise or other exhausting physical activity.

I'd say "I'm out of breath," "I need to catch my breath," "Give me sec to get my breath back," etc

If it’s due to exercise, it’s called being “out of breath.” If it’s due to a medical condition or emergency, it’s called being “short of breath.” If it’s due to an anxiety response to some stimulus or other, it is called “hyperventilation.” Some medical emergencies can cause hyperventilation, which is more acute than shortness of breath and generally feels different.

In one word: breathless. Examples: "I have been running and now I am breathless!" Or, "I am breathless from running."

Panting

The act of breathing very fast with your mouth open to maximise your oxygen intake is called panting. It’s mostly associated with dogs and the way they breathe with their tongues hanging out, but can also be used for humans in the situation you describe. Hyperventilating is more when the amount of oxygen in your blood becomes too high, often as a result of panting, or having a panic attack, or just breathing deeply over a period of time eg when learning a woodwind instrument or even when learning to swim. It can lead to feelings of dizziness.

I am puffed, is what I would say.

I’m knackered

Out of breath: 'I ran a long distance and now I'm out of breath, but I can take a break and I'll be able to run again' Exhausted/tired/knackered: 'I ran a long distance and now I'm exhausted, I don't think I can run again'. Depends on what you're trying to say, some people use all four synonymously but if you're trying to be accurate, out of breath is what I'd use.

Common phrases for this, winded, out of breath, panting

Out of breath. Winded Panting gasping for breath Breathless. also, there's a place called r/whatstheword for this advice