Suprisingly, she was never nominated for a Grammy. I know they didn't take teen artists seriously, but atleast should acknowledge her talent....then again award shows are just popularity contests and in 1990 they gave Milli Vanilli an award (thankfully taken away) ...
1988: New York Music Awards Debut Artist of the Year
Best Debut Album ("Out of the Blue")
1989: New York Music Awards Artist of the Year
Song of the Year ("Lost In Your Eyes")
Best Female Pop Vocalist
WPLJ Artist of the Year
Best Video ("Electric Youth")
1989: ASCAP Pop Awards Songwriter of the Year (tied with Bruce Springsteen)
1989: ASCAP Pop Awards Most performed Songs of the year:
"Only In My Dreams", "Out of the Blue"
"Foolish Beat", "Shake Your Love"
1989: Ampex Golden Reel Awards "Out Of The Blue" (Album)
"Electric Youth" (Album)
1989: American Songwriter Awards: Rock Producer of the Year
1990: ASCAP Pop Awards: Most performed Songs of the year:
"Lost In Your Eyes"
some more
Nominated-Favorite Female Music Performer-People's Choice Awards - 1990
Nominated - Best Pop Female Vocalist - American Music Awards - 1989
Co-host of the American Music Awards - 1989
Youngest person to ever write, produce and perform a #1 single - 1988
Also hosted the first Kids Choice Awards' though not sure if she was nominated or won anything.
"Electric Youth" was nominated for best art direction at the 1989 Video Music Awards though lost to a bad Madonna video. Ironcially, Moronic TV viewers ranked "Electric Youth" as one of the worst videos off all time in "25 Lame" (1999).
Deb will be eligable for the Rock N' Roll Hall of Fame in 2012...

Though she's already in the teen idol exhibit.
Though the record of being the youngest artist... (yeah, we all know) will never be broken since most of today's pop acts lack or have very little talent and are more focused in partying/being tabloid fodder...