did it win any awards?
Yes, the "Rhythmic Top 40 Title of the Year", "Hot 100 song of the Year" and "Hot 100 Airplay of the Year" awards.
We Belong Together
 At the 2005 Billboard Music Awards ceremony, Carey won five awards, with the song receiving awards in the "Rhythmic Top 40 Title of the Year", "Hot 100 song of the Year" and "Hot 100 Airplay of the Year" categories. 
who was mariah carey song we belong together about A woman's desperation for her former lover to return. who composed it? Mariah Carey, Jermaine Dupri, Manuel Seal and Johntá Austin. was it part of any album? Yes, The Emancipation of Mimi. was it criticized on any grounds? No. did it make it to the charts? Yes, the US "Billboard" Hot 100.
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We Belong Together [SEP] Awards and nominations
"We Belong Together" was awarded several prestigious music industry awards throughout 2005 and 2006. At the 2005 Billboard Music Awards ceremony, Carey won five awards, with the song receiving awards in the "Rhythmic Top 40 Title of the Year", "Hot 100 song of the Year" and "Hot 100 Airplay of the Year" categories. On November 6, 2005, Carey earned two awards for "We Belong Together" at the Radio Music Awards ceremony, in the "Song of the Year/Mainstream Hit Radio" and "Song of the Year/Urban and Rhythmic Radio" categories. Similarly, "We Belong Together" won the "Best R&B/Soul Single" and "Best R&B/Soul Single, Female" awards at the 20th annual Soul Train Music Awards, "Choice Love Song" at the Teen Choice Awards, "Best R&B Song" at the Vibe Awards, and "World's Most-Played Single" at the 2005 World Music Awards.