Actually, I would just like to make sure that I am right about sth. I feel very ashamed I do not know it for sure

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Is the sentence below correct, please?
I've not been waiting long.
Or do I have to say
"I haven't been ..."?I am not sure whether the first sentence would be normally acceptable and considered right.
If the sentence really is right, is there a difference between "
I've not been waiting long. " and
"I have not been waiting long."? I mean, I know there is no difference in meaning; I'd just like to know if, for example, the second sentence emphasizes the negative "not" more or less than the first sentence.