Your sentence is perfectly fine. You can also say simply "I hope I will win a prize" to mean almost exactly the same thing. "I hope so." would only be used in a response to a question or other statement. "So" is used to stand in for something else, almost like a pronoun "he" or "her" (for example): A: "I think you will win a prize" B: "I hope so." A: "Do you think you will win a prize?" B: "I hope so"

I hope I win a prize (common) I do hope I win a prize (old-fashioned) When you say you hope something, you typically say it in the present tense, ex. I hope she likes it (even if she won't see it for a while) I hope we can visit her when we are in town next week (again, it clearly hasn't happened)