I went back to reread what you wrote. You're right about the difference between moodswings and bipolar disorder, where being bipolar is connected to those specific emotions, usually either happy or unhappy, a repeating cycle.

Moodswings can be a symptom of multiple disorders (ADHD, ODD, Anxiety disorder, Bipolar disorder) but isn't a disorder on its own.
But you also wrote he hasn't been diagnosed with bipolar disorder yet, so you could just have him suffer from severe moodswings?