I can legitimately style myself an ‘award-winning writer.’ I’ve received real awards from real organizations, not ones that exist just to make money off those who enter their contests, the awards equivalent of vanity publishers.
Admittedly, my awards are for poetry, not novels or stories. I also have a box full of ribbons of varying hues — including a good number of blues — from art shows. Those are nice but have little bearing on me as an author (though I do my own design, illustration, etc).
The poetry awards? I still consider myself a poet more than a novelist, and maybe a songwriter more than a poet. It certainly colors my prose style; I consider that a good thing but all readers might not agree! I don’t enter contests anymore, and rarely submit poetry to magazines. I have enough literary magazine credits as it is.
To be honest, I dislike the idea of awards. They are quite meaningless and exist primarily as an advertising tool. I am in a competition with no one. The publicity element is hardly worth it. Mentioning an award on my site or in a blurb of some sort would be without meaning to most. However, having an award announced by some organization could provide a momentary boost in visitors who come through curiosity.
There are cheaper ways to achieve name-recognition, ways that are both more effective and more reliable. Sales, of course — the more one sells, the more one will sell! Reviews are quite useful. Public appearances might help, if one is good at that sort of thing. Maybe even if one isn’t.
This is one reason why I attempt to keep up the other creative parts of my life. Getting out and playing music makes me more visible as a writer and vice-versa. As does having an online presence and posting this sort of thing. But vanity awards? Not for me, thank you.