I'm confused about the difference between the two.
I know that "nag at" can refer to a problem that's nagging at you.
How about in this example?
One day, I nagged (at) you, and you snapped.
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The action of nagging is someone or something pestering someone else. That is, the nagger is taking action generally considered to be annoying, and the nagged person is being annoyed. However, if the person being nagged is not annoyed, are they really being nagged?
Thus, if you nag at someone, you are intending to make them annoyed. However the nuance does not communicate whether or not the person you are nagging at, is annoyed.
If you nag someone the nuance is that the person is annoyed by it.
If an inanimate article (eg a question) is nagging at you, we assume that since it is inanimate it cannot intend to nag, and thus the meaning becomes essentially the same as if you said the question was nagging you.
nag= transitive verb
Sample: One day I nagged at you and you snapped.
Generally speaking, nagging is transitive in these contexts and does not require at. But in AmE, one sees and hears "nag at", even though the at is unnecessary.
Definition of nag (Entry 1 of 3) transitive verb
1: to irritate by constant scolding or urging 2: BADGER, WORRY
I would use something like:
One day, I nagged you for hours and you finally snapped.