Agree with Debbie. Keep looking. There are certainly agents who take on PB authors who aren't also illustrators. The pbpitch website (
www.pbpitch.com) has a list of picture book agents - actually, it's probably a bit outdated, I need to do some updates, but it's a good place to start. In addition, google "Monster list of picture book agents" or something like that. That list might be more up-to-date than the PBPitch one. The MSWL website (manuscript wish list) and corresponding Twitter hash tag might be helpful as well.
PBPitch is coming up on 6/9 if you are on Twitter. Agents and editors (of mostly small houses) stop by and heart pitches. They are selective, but we do get success stories every time. :-)
Best of luck!