A few years back I tried the contraceptive injection. It didn't react well with my body at all, in fact I bled constantly for the whole 12 weeks. It wasn't heavy bleeding or anything but bleeding full stop is just not nice to have to deal with when it won't stop!!
Anyways the doctor prescribed me tranexamic acid, and at one point he also prescribed mefanamic acid. They both worked very well for me, the bleeding stopped within a few hours of taking my first dose with both of them and there were no side effects. Mefanamic acid is also an anti inflammatory, most commonly prescribed for people with very bad period pains and cramping etc, so if taking stuff to stop you bleeding tends to give you period pains then I personally would recommend the mefanamic acid, however i did do a googke search of it and it doesn't stop everyone's periods 100% apparently (although it did mine and 2 other girls i knoe eho were perscribed it) so it might be worth asking your doctor to prescribe a coutse of it and see how you get on with it.
Hope you manage to find something that works for you in time for your booking, let us know how you get on!
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