What book, movie or song can I compare with "Zenas Witt" by Edgar Lee Masters?

One must first consider what Zenas's problem is:

I was sixteen, and I had the most terrible dreams,

And specks before my eyes, and nervous weakness.

And I couldn't remember the books I read...

And my back was weak, and I worried and worried...

Zenas sees eye floaters ("specks before the eyes"), has a poor memory, and worries obsessively. In my reading of the poem, I associate his symptoms with the onset of madness, particularly schizophrenia. It's important, too, that he is sixteen, as signs of schizophrenia usually arise when someone is in their late-teens or early-twenties. 

He "worried" more after reading "Dr. Weese's advertisement," which outlined all that was wrong with him and predicted "an early grave." Perhaps Zenas read that he was likely to commit suicide. 

In the end, he does not die of this, but of "a cough," probably tuberculosis. In death, he is relieved of the "terrible dreams."

If you choose to use this reading of the poem in your paper, there are a myriad of comparisons you can make. I will list a few in each form of media that you have mentioned.

Books: Girl, Interrupted; One Flew Over the Cuckoo's Nest

Movies: If you do not care to read the aforementioned books, both were turned into films. If you like classic films, check out The Snake Pit starring Olivia de Havilland, one of the first Hollywood films to deal with the subjects of mental illness and treatment. 

Song: "Christine" by Siouxsie and the Banshees. Pay particular attention to the following lyrics: "She tries not to shatter / Kaleidoscope style...This big-eyed girl sees her faces unfurl / Now she's in purple, now she's the turtle / Disintegrating..."

I hope this helps.