This sounds like a challenging and fun assignment, and I have some advice for you.
If you choose "Wild Nights," for example, begin by reading the poem closely and annotating it. Looking at an analysis here on eNotes is a good second step, and I've copied the link below. Next, I would advise taking your research a step further as your teacher has suggested, to find another published, scholarly interpretation. For "Wild Nights" you could look at Brooklyn College Professor Lilia Melani's page. The link is below.
An important part of this assignment is finding a credible interpretation by a published academic. If you want to look beyond what I have described, The Explicator is an excellent, highly regarded journal with short analyses and interpretations of all kinds of literature, including Dickinson's poems. There is a search bar on their website that allows you to search by poet and title. Your school may have a subscription, so checking with your librarian is a good idea. You can also use the email link on the site to ask for permission to use the article. The website link for The Explicator is below.
Be very careful about where you seek critical interpretations. There are all kinds of blogs and student help sites of varying quality, so you might want to ask your teacher what kinds of sources are allowable. I would guess he or she wants you to look at scholarly journals as I have described above.
Your final step would be to reread the poem and develop your own thoughts about the interpretation(s) you've read, and then compare and contrast your findings. Be careful to cite your sources to be clear what is your thinking and what you have taken from others' work.
Good luck, and happy reading!