Unfortunately, your situation is a common one. Most people who live with bipolar disorder spend more time feeling depressed than they do feeling speeded up or manic. And traditional mood stabilizer medications—like lithium—are generally more effective for controlling or preventing mania than for controlling or preventing depression.
For people with bipolar disorder, use of antidepressants is controversial. The largest study of antidepressant medication for depression in bipolar disorder found it was—on average—not better than a placebo. For some people, though, antidepressant medications may help reduce symptoms of depression without increasing risk for mania or mood swings. But for some people, antidepressants clearly do bring on mania or more unstable moods (“rapid cycling”). It sounds like you are one of those people who should probably avoid traditional antidepressants.
There are other types of medications you could take along with lithium that might help more with depression. Lamotrigine is a mood stabilizer medication that may help more with depression than lithium or other mood stabilizers. Two of the newer “atypical” medications (Lurasidone and Quetiapine) have been officially approved to treat depression in people with bipolar disorder. Research suggests that some of the other “atypical” medications may also help with depression in bipolar disorder, but they are not specifically approved for that purpose. As you probably know, medications for depression often take two weeks or longer to help. And different medications work for different people, so trial-and-error is sometimes necessary.
Medication may not be the most effective treatment for depression in bipolar disorder. The same large study that found antidepressant medication was not effective for depression in bipolar also found that specific kinds of psychotherapy were clearly effective. Those psychotherapy treatments (Cognitive-Behavioral Therapy, Interpersonal and Social Rhythm Therapy, and Family Focused Therapy) reduced depression in the long term without any risk of more mania or mood swings.