is there any downsides to using birth control to stop menstruation?
If you have access to medical care, please ask your doctor this question. Every single medication, drug, herbal supplement, food, etc (essentially everything you put in your body) has its potential up-sides and down-sides, and many (perhaps most) of them have to be evaluated in the context of your current medical status, including weight, BP, family history, other things you are taking, and a lot of other factors.
I agree with Turbo. While Moonbear, Adrenaline and Doc Toxin are probably the best qualified to respond, I'm sure that all of them would refer you to your personal physician. We're not shy or coy or embarrassed about discussing things like this, but nobody here is capable of answering personal medical questions which require insight into your own medical history. There are far too many factors involved which cannot (ever) be dealt with over the net. If anyone tells you otherwise, s/he is lying and should be ignored. Talk to your doctor.
As has already been indicated, you would want to discuss with your personal physician any specific concerns or risks related to your own medical history, the specific form of birth control you will be using, the duration of use, other medications you may be taking, etc. You can also talk to your pharmacist about potential side-effects, contraindications, and any potential drug interactions (for example, you should know that some antibiotics can reduce the efficacy of oral contraceptives, so if you are taking antibiotics, you will want to either use an alternative form of contraception or abstain during the full cycle following use).
In more general terms, there are inherent risks to all hormonal contraception, and some people are at greater risks of side effects than others. For example, all hormonal contraception in the U.S. comes with a warning of blood clots, which can lead to stroke or pulmonary embolism, as a serious side effect. This is a rare side effect, but your risks are greater if you're a smoker, or already have a predisposition to a clotting disorder. (I will note that the progestin-only contraceptives, i.e., Depo-Provera, do not carry this warning in other countries, and the scientific literature indicates it is the estrogens that primarily are the risk factor for blood clots, so I do not know if the labeling requirement in the US is based on known side effects, or just a blanket "cover our butt" warning the drug company lawyers told them to include.)
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