Most of the songs I found with those lyrics are by female performers (see below).
Without more to go on, you're gonner have to run the gauntlet...
"Look Me In The Eyes" by The Jonas Brothers
"Look Me In The Eye" by J. GEILS BAND
"Unsatisfied" by Replacements (or Counting Crows)
"There's A Face" by Eve 6
Female performers:
"Look Me In The Eye" by Lisa Loeb
"Are You Happy Now" by Michelle Branch
"Look Me In The Eye" by Margaret Becker
"Where Does The Good Go" by Tegan And Sara
"Look Me In The Eye" by The Donnas (feat. Steven Michael Huber)
"Look Me In The Eye" by Disney (female?)
"In The Eye" by Suzanne Vega
Them that can, do; them that can't... memorize Artist and Title