About a day before I get my period, and then when I have my period, I get extremely depressed.

I show almost all the signs of depression during this time, and then they all disappear after my period ends, although I do get headaches when it ends for a few days.

I show no symptoms of PMS and no symptoms of depression during the rest of the month.

What might this be?

It is just your hormonal imbalance shift right before you period.

As long as the depression doesn't last beyond your period, and as long as it's not severe depression with thoughts of suicide... it should be fine.

If you are concerned, however, consult your doctor.

It sounds as though you could have what is called PMDD.

Here is some more info on it. It is treatable.

Premenstrual Dysphoric Disorder (PMDD) -- familydoctor.org