I am not sure who diagnosed you if you are yet to see a psychiatrist. It is not the kind of a diagnosis that is normally made by therapists alone. Also, manic depression and bipolar are the same thing. Manic depression is the old term, and bipolar is the new term. Since you did not know that, it appears that your diagnosis is brand new (well you said so), and that whoever made the diagnosis did nothing to educate you (since you are confused and think of them as two separate things). So the first thing you need is a good treatment provider who would educate you better and diagnose you with better precision, especially since given your young age, diagnosing bipolar is not straightforward.

To the mom: do not tell her NO. Tell her that you would love to help but it would be dangerous to leave two young girls in your care when your mood is so unstable. tell her that you hope to get better with treatment and therapy and will let her know when you are able to resume watching the girls, and, that it is your goal to get better and resume babysitting your nieces.

This way you won't hurt her feelings.