I’m all right, Jack
Definition 1 of 2
Pro Tip 1/3Personal Assurance
Use it to reassure someone that you're fine and need no assistance. 
After the minor bike accident, I got up and said, 'I’m all right, Jack.'
Pro Tip 2/3Not a Distress Signal
It's not appropriate for situations where you actually need help. 
Even though he was lost, he told the guide, 'I’m all right, Jack.'
Pro Tip 3/3Colloquial Context
It's casual speech, suitable for informal conversations, not formal situations. 
In the friendly get-together, when offered more food, she smiled and said, 'I’m all right, Jack.'