If you have bipolar illness do you see a psychiatrist or a psychologist?

Psychiatrist/both. A psychiatrist has the medical training to allow medication prescribing which is necessary for most bipolar pts. Psychologists can provide excellent adjunctive psychotherapy which can help you to learn better coping skills and overcome bad habits.
Added comment . You may also want to be in a support group or in group therapy. Help from your fellow patients can be an additional therapeutic step.
Eval. Get a full psychiatric evaluation for bipolar disorder. If bipolar disorder is found, then medications, typically mood stabilizers will be prescribed. Therapy is also strongly indicated. If The evaluation is negative for bipolar disorder, medication still may be needed. In that case therapy is also strongly indicated.