No you don't need to refer to all the poems in your essay. Best to only refer to two or three (if you're using the shorter ones) and go into depth with those.
I wouldn't just have notes on those though, I had notes on 4 for the HSC so I could decide in the exam which poems and which of my concepts could best answer the question. Of course you can't do that if you're planning to pre-prepare an essay..
This is my Letter is about wanting to belong to society but their rejection of her, her belonging to nature and belonging through her art-form (writing) and therefore to posthumous audiences rather than her present. Hungry shares the idea of the innate need/want to belong to society, but in it she realises that she doesn't actually need society because it causes her fear/pain, and she can belong more comfortably in nature and from within.
Sooo when I used these poems I focused on the concept of internal belonging~ to nature and to her writing, and the fact that she didn't need society to get a positive sense of belonging.
'Walden' by Thoreau is a biography that you could use, specifically the chapter on nature, because he's promoting solitude. 'Letters to a Young Poet' by Rilke is similar- promotes solitude to enhance writing and internal connection. Hm, 'Bright Star' is a film by Ana Kokkinos about John Keats (Romantic poet) and Fanny Brawne, and how nature and writing allow them to belong despite physical barriers.. and the ability (in the end) to have belonging through nature and poetry even after death. I also used Steppenwolf, a novel by Hermann Hesse about a Schizophrenic (sort of) man who believes his soul is half wolf (nature) and half man (society) and it deals with the struggle between then two and the inability for him to belong in bourgeois world due to superficiality.
UMmmmmmMmMmmmmm I'm sure there are a million more. 'The Love Song of J Alfred Prufrock' also works for proving these sort of ideas by reflecting the opposite- when one does not have nature, and instead lives in an urban wasteland, one's sense of belonging is corroded. Prufrock also can't connect with his superficial society, like Dickinson who can't connect with her Calvinist religious context.
You don't need to find texts that deal with nature either, but I found it easier that way. Hope they helped, but better to find your own related texts that you're already familiar with.
Good luck ;D