Those terms all refer to bipolar mood patterns, meaning patterns that include both periods of low or depressed mood and periods of elevated mood or over-activation. The specific terms describe different levels of severity.
Cyclothymia refers to a bipolar mood pattern including both depressed periods and elevated periods when both are less severe. Depressed periods are not severe enough to be called major depressive episodes, and periods of elevated mood are not severe enough to be called full manic episodes.
Bipolar II disorder refers to a mood pattern where depressed periods are more severe but elevated periods are less severe or briefer. Depressed periods do include several symptoms of depression, last at least two weeks, and cause significant interference with daily activities. But elevated periods are milder or briefer and have not led to hospitalization.
Bipolar I disorder refers to a mood pattern where both depressed and elevated periods are severe. Technically, a history of a single full manic episode means a diagnosis of Bipolar I disorder, even with no history of depression. In reality, however, almost everyone who experiences a full manic episode also has had episodes of depression.
Regarding the need for continued medication, the real question is the risk of relapse (into depression, or especially into mania) if you are not taking maintenance or prevention medication. People with Bipolar I disorder are certainly at higher risk of relapse into mania. Risk also depends on other individual factors, especially the number of severe mood episodes a person has experienced and the time since the last severe episode. As you mention, a history of psychosis also indicates higher risk.
Before making any decision, you’ll want to carefully review your history with your doctor. It’s possible that she did not understand or accurately record some of what you reported. Or it’s possible that she has observed mood problems that she thought were more severe than you did. Coming to a shared understanding of your history is important, not only for accurately understanding your risk of relapse but also in understanding what to watch out for if you do make a change in medication.