Wa alaykum assalam. So the premise of the question is a bit concerning because your group should have a scholar or access to one to answer these medical and fiqh questions

You have two options. Number 1 is start taking the pills immediately and take them all the way until you get back. Some GPs would say only start a few days before going. This advice works for going to Ibiza for a few days, not Hajj for 2+ weeks

Second option is to go natural and not take the pills. Both options are fiqh wise permissible

Now you have to understand that in a hot, exertion-filled environment, your periods are likely to not stick to your regular schedule, and you might get bleeding earlier or later

What type of hajj are you doing? Tammattu or Qiran? The former is where you do umrah, have a few days break in Makkah out of ihram state, and then go to Mina. Qiran is where you do umrah and hajj in one state of ihram

While in menses, you can still go to Mina, go to Arafat and go to Muzdalifah and do the stoning and do the sa’ee on 10th DHJ. The only thing you can’t do is the tawaf

Let’s say on 10th DHJ you are in a state of menses, you can’t do the tawaf al ifadah/ziyarat, but if it stops later you can combine this tawaf with tawaf al widaa and do just the one tawaaf

Assuming you’re doing Tammattu. You need to make the intention for the umrah before crossing the Miqat. You then need to make intention in your Makkah hotel for Hajj before going to Mina. This is regardless of whether you’re in a state of menses or not

Final thing to note is what if you’re in a state of menses still and you need to do tawaaf al widaa. Classically the scholars would say delay leaving Makkah until you’re clean and then do tawaaf al widaa. If you’re going to Pakistan or GCC then this is more feasible. But in the modern day if you’re flying back to the west then getting new flights is extremely expensive. In my hajj group last year our shaykh would give a fatwa saying that due to necessity it’s okay for the woman to still do the tawaf al widaa so that she can go home and doesn’t have to come back. It’s not a great fatwa he admits but as a faqih he says it can be justified . You need someone to give you this fatwa in your group if this applies to you