are a common problem. Many women your age will develop them, especially after pregnancy. Regardless, this warrants evaluation by your primary care doctor
or OB / GYN. There are some inconsistencies in what you describe which suggests that you may not have classic hemorrhoids.
Hemorrhoids are enlarging of the blood vessels that supply the anus with blood. If there is increased pressure in the pelvis, say from your child, that the vessels can increase in size as they become congested. There are two type of hemorrhoids, internal hemorrhoids and external hemorrhoids. Internal bleed but rarely cause pain. External can cause pain, but often don't bleed as much. Internal are far more common. If you were to have external hemorrhoids, as suggested by the pain, these may need to be addressed surgically as if they thrombose (become clotted) this can cause severe pain.
As to why they worsen during your period, this is fairly common. The hormones during your period can cause relative constipation. This is because the muscles are relaxed in the colon by the hormones. The harder stools can cause more bleeding
as they rub past the hemorrhoids. Therefore, keeping your stool soft (with fiber) is important.
See your doctor. This can be evaluated and hopefully treated. Good luck!