My friend went through a lot of the same things you are describing after her 2nd daughter was born. (The part about being afraid something bad would happen if she left is almost word for word).
She saw a doctor and was diagnosed with anxiety DO. Took Effexor for about a year and then weaned off of it and just relied on psychotherapy and three years later she is doing great!!!
When I decided I needed to get help (I started with psychotherapy) I had to wait a week for my appt too, and it seemed like forever. If you are afraid you will forget the appt, can you have your husband or a friend call you the morning of and remind you? I have this problem too, I miss appts all the time. Some people say setting an alarm on their phone helps. Another girl told me if you have an iphone you can take a screen shot of the appt reminder and set it as your wallpaper so you see it every time you pick up your phone (my phone doesn't do that).