It's almost impossible to break into a successful career as a lyricist because the competition is so massive.
Messrs. Taypin and Barlow are both connected to hugely successful artists, and they are paid an agreed royalty every time a song they have written is bought, or played anywhere in the world - hence thier millionaire status.
But ctances like that come along once in a blue moon - you need to be connected to a band or singer from Day One, and for them to be a success - it is almost unheard of for a writer to simply have their work recorded my major artists, although Dianne Warren does this, but she is one of very very very few who can. Check out the sort of talent you are up against -
http://en.wikipedia.org/wiki/Diane_Warren
But it can happen. The breaks are a matter of luck, and definitely 'right place, right time'.
Why not hook up with any bands in your area, and see what you can do together? You may at least have the thrill of hearing your songs in your local puba, and remember,e everyone starts somewhere. I recall beginning my music journalism career in the early '80's, and a friend telling me of a New Romantic band who played at their manager's club where the guitartist was the burger chef, and they would love an interview. I told her that unknown bands are hard to sell, and she asked me for weeks and weeks, and I never did get to talk to that unknown band who were desparate for an interview anywhere.
What ever did happen to Duran Duran?