This is a fun assignment! I have some tips for you I think might help you in writing your poem.
Luckily, Emily Dickinson has a very simple rhyming style that she tends to use in her poetry.
Here's an example, "I measure every Grief I meet" by Emily Dickinson
I measure every Grief I meet
With narrow, probing, eyes –
I wonder if It weighs like Mine –
Or has an Easier size.
I wonder if They bore it long –
Or did it just begin –
I could not tell the Date of Mine –
It feels so old a pain –
I wonder if it hurts to live –
And if They have to try –
And whether – could They choose between –
It would not be – to die –
I note that Some – gone patient long –
At length, renew their smile –
An imitation of a Light
That has so little Oil –
I wonder if when Years have piled –
Some Thousands – on the Harm –
That hurt them early – such a lapse
Could give them any Balm –
Or would they go on aching still
Through Centuries of Nerve –
Enlightened to a larger Pain –
In Contrast with the Love –
The Grieved – are many – I am told –
There is the various Cause –
Death – is but one – and comes but once –
And only nails the eyes –
There's Grief of Want – and grief of Cold –
A sort they call "Despair" –
There's Banishment from native Eyes –
In sight of Native Air –
And though I may not guess the kind –
Correctly – yet to me
A piercing Comfort it affords
In passing Calvary –
To note the fashions – of the Cross –
And how they're mostly worn –
Still fascinated to presume
That Some – are like my own –
She has what is called "common meter", with 8 syllable and 6 syllable lines going 8686, like in the song "Amazing Grace". She also uses rhymes that aren't EXACT rhymes of each other, so there is a lot of room to be creative.
You should choose a topic that interests you. Dickinson tends to write poetry with darker themes, even when she's talking about her own identity or her love life. The topics they gave you as examples are self identity, nature, death & immortality, and love.
Do any of these jump out to you? Maybe you have a hard time defining your identity. You could write about the struggle to know exactly who you are. Maybe you have strong beliefs about death and the possibility of an afterlife, and you'd like to write about that. You could write a cool poem about how you're nervous about death and dying, or about how you're not nervous at all because of the afterlife you believe in.
The key is to put in your own personal feelings, negative or positive.
Use lots of "I" and "me", and try writing it in present-tense. For example, "I walk along the lonely road, the fog rises around me / Death crosses into my path / I turn away and ignore his presence though the leaves have begun browning"