Using "not only" without clarifying what else was done

Consider the sentence:

I did not only go to the store.

It has the same meaning as

Going to the store was not the only thing I did.

Is the first sentence grammatically correct, or do I need to add an independent clause to it?

Solution 1:

I did not only go to the store.

The sentence is grammatically correct, but it does beg a second clause or sentence(s).

As in: Google Books

Going Down Under Over

I did not only go Down Under.

The second sentence cited from Google Books:

It is a great story to show how God took my family to Australia.

In context I would suspect the next sentence(s) would explain what else one did on the trip to the store.