You have a decent start with the # of lyrics you've written, but what you're talking about is an uphill struggle, so be aware... first, nobody (with a capital "NO"), in the industry is looking for lyrics only, so approaching record companies and/or semi-established artists looking for co-writes is pretty much out of the question. The other thing about that is that it doesn't matter if you're lyrics are "better" than what you hear on the radio. In pop & r&b the lyric is a distant second to the music, and even in country, which is much more lyric-driven than the others mentioned, the music is a huge consideration. In either case, the lyric is often judged on the basis of style and tone and how appropriate it is for a particular artist. Everybody wants songs that are ready to record... the way is much brighter if you can hook up with a composer who will co-write with you and help push the finished songs. Better yet, if you can hook up with an up-and-coming performer who needs help on the lyric-side. None of this should discourage you, just make you realize that you have a certain amount of business & networking legwork ahead of you to get where you want to be.
Generally composer & lyricist share 50/50... the finished song would be registered with both persons as authors. If you've already registered the lyric by itself it might require a revision of some kind, refer to www.copyright.gov... I would only worry about the laws of the US (because it's the biggest market, and the laws are peculiar) and whatever country or countries you're actually operating in.
There are a lot of people who offer to compose music for a fee, and you shouldn't bother with these, because generally the music isn't very good, but that would be a work-for-hire (get it in writing), and no authorship rights would go to the composer. A legitimate co-write shares expenses and proceeds 50/50, as mentioned above. I can't imagine a situation where money would change hands before a song is ready to demo. Which is another thing to watch out for, people who offer to compose music for you, and make you pay way too much for a poor-quality demo...