Hi & Welcome to HCM.
I can understand your problem.
Birth control pills do not cause
constipation.
However, the excessive use of laxatives may decrease the efficacy of birth control pills and should be avoided.
After having gone through your problems described in your query, I am of the opinion that you appear to have some sort of tear in the anus referred to as "fissure in ano" which is reflected in the form of painful defecation while passing hard stool and sometime tinged with blood.
A surgical consultation is recommended for proper clinical examination and to rule out other anal conditions like hemorrhoids, etc.
Meanwhile you may take plenty of oral fluids, eat plenty of green leafy vegetables, avoid carbonated soft drinks, meat, etc.
For pain following defecation you may use local
anesthetic containing creams like Faktu (to be applied before the act of defecation).
Hope to have answered your query.