It can be very difficult to tell the difference between ultra-ultra rapid-cycling bipolar and borderline pd. Some people even argue that BPD is itself a bipolar spectrum disorder. Both disorders are very heterogenous and present uniquely in each patient, which further complicates things!
I wouldn't worry too much over which disorder you have; it truly is an exercise in "splitting hairs". The most commonly used treatments for each disorder can help people with the other (many borderline pts are on mood stabilizers, and many bipolar pts have benefited from DBT...hmm, this seems to further support a relationship between the two illnesses...) so try to focus on treatment. Avoid antidepressants if possible.
I know that BPD has a very high stigma attached to it, so I can understand why you would want to rule it out. However, regardless of whatever your therapist (or sadly, even other people with mental health problems) think(s), borderline patients are not monsters. If it turns out that you are borderline, your illness is just as real as bipolar disorder, and it is no more a part of who you truly are than bipolar is a part of who I am. If you are actually borderline, be proud of yourself for dealing with a very serious and aggressive illness; don't be ashamed of the label.
Cyclothymia would not cause psychosis, so if you are bipolar you probably have a different type. Also, the depression experienced by cyclothymes is by definition milder than major depression. BPD can cause transient psychosis. So can mania in bipolar I and depression in both bipolar I and II. People with schizoaffective disorder experience psychosis even in the absence of mood symptoms.
I hope this helps with your differential, but try to remember that treatment is more important than diagnosis.