Thank you for your question. It is my privilege to be able to help you.
First of all, please do not be concerned about the hair falling out. During pregnancy, many women grow a thicker fuller head of hair, because the cycles of hair growth are changed by the pregnancy hormones. Usually, several months after having a baby, these cycles get reset back to normal, and many women experience a period of hair loss. It will recover soon, and you will get back your beautiful hair.
As far as the period is concerned. If you are breastfeeding, it is very common to not have a period for a while, even six months or even a year or so as long as you are breastfeeding.
If you are not breastfeeding, then your periods will usually return to normal around 6-8 weeks after the delivery or after you stopped breastfeeding (if you did breastfeed for a little bit). It will usually return to what is normal for you, so if you occasionally skipped months and had irregular periods before, the same pattern will probably return.
You should also consider the possibility of pregnancy. if you are not using birth control and have been having unprotected sex, you should consider the possibility that you are pregnant again.
I hope you find this helpful. If you have any more questions please feel free to ask me. If you are satisfied, please remember to ACCEPT the answer so that I get credit for my work. BONUSES and positive feedback are always appreciated. Good Luck! Dr. SaulJE