Near by is not commonly used in this sense by native speakers.
Nearby, although also an adjective, is more common as an adverb. As in:
She lives nearby.
Also, while being used as an adjective, it's uncommon to use an article after nearby. See the example sentences in oxford:
But Mr Dodsworth claimed that nearby residents had all been in the
He believes that nearby shops may be using the banks to dump
And the copper giant has also adopted three primary
health centres in nearby villages.
You see the pattern? The creek nearby the grocery store doesn't quite sound right.
According to oxford, near to is equivalent to near (the proposition).
(also near to) At or to a short distance away from (a
the car park near the sawmill
do you live near here?
[SUPERLATIVE]: the table nearest the door
The third sentence is correct.
He went fishing in the creek near to the grocery store.
But a native speaker is more likely to drop the pronoun.
He went fishing in the creek near the grocery store.