I came across a problem that hope to be solved by your helps!
What does the following sentence mean?
"I'm about to do something!"
You give it as a complete sentence, and with an exclamation mark which makes me suspect this is out of context.
Where did you find the sentence?
Sounds like, for instance, the euphemistic cry of somebody about to wet their pants.
Now, a question is still standing is when are we allowed to use it?
This structure is often used with 'just' to show that the action is coming rather soon after speaking.
A: [phones B] Hello, B. Can I come over for a visit?
B: No, that won't work, A. I've got my coat on and I'm just about to go out to the mall. Why don't you meet me there?