You are absolutely right that the vast amounts of information on Sigmund Freud (or Anna Freud?) and Melanie Klein can be overwhelming. You can’t possibly read everything. The challenge for you is to figure out how to focus on the relevant sections of Freud and Klein, the sections that relate specifically to your field of study. Enotes.com has a number of good general overviews of Freud and some discussions of Klein. I’m providing links for both. In addition to reviewing those overviews, you may have luck with specialized encyclopedias for education and psychosocial psychology. You will likely find that the most relevant overlap between Freud and Klein in your field centers on their very different analyses of children’s play.
Above all, I would recommend that you consult with your university’s librarians. As a student enrolled in a masters program, you have access to your university’s library and are expected to use it, even if your professors haven’t said so clearly. The librarians themselves are probably the best resource for you. Most universities has librarians who specialize in the different disciplines. Speak with librarians at your university, identify yourself and your masters program by name, ask if there’s a librarian specializing in your area, and explain that you need assistance in locating introductory materials on Freud and Klein’s differing ways of making sense of children’s play. Librarians are amazing. They will likely be able to help you on the spot to search the library databases (using good key words in these searches) and identify some very good resources that you can check out, read in the building, or order through interlibrary loan. Speak with the librarians as soon as possible, as good research can sometimes take time, particularly if you need to order materials from elsewhere.
I hope that these suggestions are helpful.