What kind of poem is this?

You actually don't need to bring anything out of it...it's already poetic because of how you created your images. If you want to "add" poetic devices, then you can reword certain sections...for example, you could have your sleek legs "peek out" or "stare out" at your mother...that would be personification...or you could speak of how they spat blood drops or lines on the sheets...again, personification. The same would hold true for the razor...you could personify the razor's actions, and add simile by saying, "like a ..." or metaphor by saying something like "the razor's wiped its sharp smile across my skin". No need for refrains and I wouldn't try to make this into a sonnet...it works just fine the way it is. I would, however, clean up the punctuation (question marks for example) a little, and I'd either put "Barbara Drake" in quotes or include it after "mother said"...otherwise it's fine.