For the most part an author should try to conform to grammatical conventions as that makes it easier for people to read. However, this isn't a set in stone rule. You are free to violate "proper" grammatical conventions in both first-person and third-person narratives. It is best if you have a decent grasp of the conventions you violate—that knowledge will help you know when you can get away with breaking a certain rule and when you can't.
As for your sentence, it is perfectly acceptable if it fits the character who is saying or thinking it. Consider the examples below to see how two famous writers handled this sort of speech.
James Joyce's A Portrait of the Artist as a Young Man opens with "Once upon a time and a very good time it was there was a moocow coming down along the road and this moocow that was coming down along the road met a nicens little boy named baby tuckoo..." That novel is a third-person narrative and the diction changes as the main character grows up.
William Faulkner's As I Lay Dying is an excellent example of multiple first-person narratives where the diction changes to match the character speaking. Some of the characters talk more "proper" than others. For instance, take a section from Darl's point of view:
Pa leans above the bed in the twilight, his humped silhouette
partaking of that owl-like quality of awry-feathered, disgruntled
outrage within which lurks a wisdom too profound or too inert for even
thought. (Faulkner, As I Lay Dying)
Now compare it with a section from Anse's point of view:
Durn that road. And it fixing to rain, too. I can stand here and same
as see it with second-sight, a-shutting down behind them like a wall,
shutting down betwixt them and my given promise. I do the best I can,
much as I can get my mind on anything, but durn them boys. (Faulkner, As I Lay Dying)