It's all in the eyes. The speaker in this poem feels alone, isolated and free from the outside world. Still, she also feels threatened, vulnerable, exposed to something out there that's watching her, that wants to hurt her. The image of the eyes is one way she expresses that fear, because the eyes in this poem are weird. They grow out of things that definitely shouldn't have them – namely, tulips.
Line 47: As we see it, this is a kind of light version of personification. The sun doesn't have eyes, and neither do tulips, so just by including eyes in this line, she gives us a pretty good idea of how warped the world seems to the speaker in this moment. Plus, think of how vulnerable she must feel, in this fishbowl where the sun and the tulips stare at her incessantly.