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I only use it speaking of something that has just been done, i.e. in the very near past.
I've finished washing the dishes just now.
Can it be used also speaking of something that is about to be done, i.e. in the immediate future?
I am going shopping just now.
The short answer is no, you can't use "just now" to refer to the immediate future.
However, you can use "just now" to refer to the action in progress (in the present). So your second sentence, while not common, is not strictly wrong (depending on the context).
For example:
A: I see that you are on your way out the door. Want to grab a coffee?
B: I'm sorry, I can't. I'm going shopping just now.
A: No problem. Maybe later.
The reason that this works is because the action is in progress (present progressive tense). By contrast, a future tense would not be appropriate:
*I will go shopping just now.
*I will be going shopping just now.
