Hi Jackie-

I see you are low on funds....
I haven't used the Songwriter's Market recently and can't guarantee that the SM will get you a cut; same goes with any other companies mentioned here, or elsewhere. But, you can find the SM or maybe other publications that have listings in a major bookstore, or local libray. Try thumbing through a couple. Copy down some names & numbers...that won't cost you any money.

If you find any publishers give then a call and research them. It's free and can be a good start. Many of the publishers give critiques on your songs, which can be very helpful to improve your songwriting. Remember, the SM has many useful articles which can be invaluable in songwriting and the music biz. There are other ways also to find listings and publish your song without paying a fee. Try that library, a bookstore, or do a search and see if any work for you.
At least you'd be doing something other than nothing.

~C~