Re: depression & baldness
You could ask your doctor what they thought about your moods. Are they related to your periods? They used to call it PMS, but now have another name for it ( I think it's premenstrual dysphoric disorder, but don't quote me on that), and it is recognized as a treatable condition. You could take a depression questionnaire on one of the depression web sites as a screening tool, but ultimately you should seek professional advice.
About the hair thing--- not quite sure what to make of that. Is it itchy? OR red? Or oozy? Is the skin there scaly? I would go back to the doctor to let them re-evaluate the situation, and perhaps send you to see a dermatologist, who can do a skin scraping to look for fungus (or maybe your doc can do this, it's a simple bench test).
I would also ask your doc to check your thyroid. Sometimes a malfunctioning thyroid is the cause of hair loss, and also depression.
Hope this helps.