Is prose considered a form of poetry or an altogether different form of writing? Can I submit a piece of prose to a poetry contest?
Well considering prose and poetry are the only two distinctly general categories in writing... no, you can't. When writing is broken up in the most general way you get poetry and prose. You can break up those two in multiple forms, but as a whole, poetry and prose aren't the same.
I've moved this to the Writing Issues -> General Writing forum, because it is not a piece to be reviewed. In answer to your question, prose is not necessarily clearly distinguishable from poetry. Prose does not necessarily mean fiction or a story, it simply means the writing doesn't distinguish it significantly from ordinary speech. You could enter it into a poetry contest, provided it falls within the stated guidelines of the contest. But rest assured, those who judge or vote in the contest will be evaluating it on the basis of poetry, as well ad any other constraints or guidelines stated for the contest. Worse yet, you will begin to build a reputation as someoe who doesn't know how to write within directed constraints. That kind of reputation will not help you when you submit other writing.