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Sorry to hear about what you have been going through.
Based on your symptoms, I would be concerned that you may have a mood disorder known as bipolar disorder, but there are other possibilities as well. First, after giving birth to a child, it is common to develop depression. This usually goes away within weeks to a few months, but in some cases it can continue for longer. This may have been the trigger for your mood problems. Adjusting to life with a baby and giving up your regular night-time sleep can also add to this problem. However, the mood "swings" that you describe indicate this is more than just simple depression.
When someone has periods of racing thoughts alternating with depression/irritability/anger, many times the problem is bipolar disorder. This is a problem caused by changes in your brain chemistry and may run in some families. It can usually be controlled with medications and counselling. When you see a doctor, he or she will likely also want to make sure there isn't another medical cause for your symptoms which can "look like" bipolar disorder, such as a low thyroid hormone. They will probably check some blood tests to rule out things like that.
I think that your description of your symptoms was very good and would be helpful to a doctor trying to determine what is going on with you. Don't worry about trying to describe your symptoms using medical terms--honestly, doctors prefer if you just tell them what you are experiencing in your own words. If you have a primary care doctor you can first make an appointment with him or her, but they may end up referring you to a Psychiatrist or clinical psychologist for further treatment.
I hope this has helped.