does posting my poetry up on cosmo count as publishing them?

Hello Krystyn,
In the vast majority of cases, if a poetry competition/contest stipulates that your entry must be unpublished, they mean that it can't have appeared in books, magazines or on websites. Which means that anything you've posted here on Cosmo is invalid.
So to answer your question, Yes...posting it on Cosmo counts as publishing in this instance. I'm afraid you'll have to write something new and enter that.

Good luck with it!

J ;)