As regards the issue of taking birth control pills to stop period during Hajj and its effect, Sheikh Ahmad Kutty, an Islamic scholar, states:

“… although some scholars permit it, I personally do not believe it is a good idea to interfere with the natural order of things; menses is what Allah has decreed for women; all of His decrees conform to His infinite Wisdom; so to interfere with it may be harmful for us in the long run. So there is no need to do that.
However, if you did take the pills and you experienced spotting and it resembles menses in color and texture, then it shall still be considered as menses; if it is not, then it shall not be considered as such.
You do not need to be worried about your hajj while menstruating; for while menstruating, you are able to do all the rites of hajj except tawaf. In case of tawaf also there are certain dispensations or concessions allowed, in case of extreme necessity.

A menstruating woman is exempt from tawaf Al-wada if she cannot postpone her journey.
In case of tawaf Al-Ifaadah, which is a pillar, she can do tawaf in a state of menstruation, after cleaning herself and wearing tampons, if she cannot wait in Makkah until such time that her menses stops and she is able to purify herself; this may be the case if she has no choice but to leave with the group she traveled with.

In this exceptional case, because of necessity, she is allowed to perform tawaf, while menstruating; for the condition of purity for the validity of tawaf can be waived in this case. The rule of Sharia is: a condition on which the validity of an act of worship is dependent can be waived if it is impossible to fulfill because of circumstances beyond one’s control. An example for this: Covering `awrah or facing the Qiblah are conditions for the validity of salah; but they can be waived in cases where a person is prevented from fulfilling them because of conditions he has no control over.

This is the view authenticated by some of the great imams and jurists such as Abu Hanifah, Ibn Taymiyah, etc.
So you may do yourself a great favor by seeking to understand the infinite mercy in the Sharia, which takes into account all circumstances.”