This is a great question. Let me give you some suggestions that will get you started.
First, you might want to start by thinking about whether you think that an Utopian Socialism can even exist. Is this a pipe dream with no basis in reality?
Second, it is always good to have conversation partners. So, think of some works that you read in class and interact with them in your essay. You can disagree or agree with them. For example, you might want to interact with Thomas More's book, Utopia. Another way to approach this topic is to read dystopian books. This will give you another perspective. These points will certainly get you started and give you many ideas.
Third, since you are in college, you should also do some secondary reading in scholarship. Your library should have databases for articles. Go on to them (Jstor is good, as is Project Muse), and type in key words, like utopia and dystopia. These will generate a lot of articles and you will be able to interact with them. Best of luck!
I think the term "utopian socialism" may be giving your trouble. It is almost an oxymoron, because socialism by its nature is utopian. It promises a society in which everybody will be provided for and everybody will be happy. Therefore, I suggest that you drop the word "utopian" and focus on socialism. If you are pressed for time, the best book to consult is To the Finland Station by the prominent American writer Edmund Wilson, published in 1940. It presents the history of socialism from its beginnings and an overview of socialist and communist thought right up to the arrival of Lenin at the Finland Station in St. Petersburg during the Russian Revolution in 1917.
You can get an overview of Wilson's classic work by consulting book reviews published in 1940. You can trace these reviews by consulting Book Review Digest in the reference department at your college library. You should find reviews in The New York Times and The New York Review of Books, among others.
I am just suggesting how to get started, as you request. You could begin your paper by offering a definition of socialism. You might want to tell how it differs from communism. You might discuss what socialism has promised and why it has never worked. There were a number of socialist experiments in the United States. None of them lasted. Why? If everybody would cooperate they could build a utopian society, but everybody will not cooperate--that's human nature. Some people work hard and other people don't want to work at all. Some people are gifted, others are not.
You say, "I don't know where to start." I suggest that you start by googling To the Finland Station and focus on socialism, not utopian socialism.