You should definitely be using backup contraception *anyway* if you're in the first month to two months of taking the Pill (one month minimum, I recommend 2), simply because it takes the Pill some time to affect your body chemistry enough to work.
In re: nausea -- I can't say for sure whether the Pill would necessarily get thrown up if one did vomit shortly after taking it, but there is a strong likelihood that it might. Whether that actually happened or not would probably depend on many circumstances, though. If you do end up vomiting shortly after taking the Pill, I would treat it as if you had missed a day, and continue taking your Pills on schedule while using a backup method of contraception as well.
And as always, I am compelled to point out two things:
1) The Pill only prevents pregnancy, not STDs. Using condoms when you have sex, even when you're on the Pill, is always an excellent idea.
2) All forms of birth control have some failure rate. By combining the Pill and condom use, you will have just about the highest effectiveness rate of any birth control available. I strongly recommend that combo, it's a good one for many reasons.
As for nausea: many people find that ginger and peppermint are good anti-nausea agents. Candied ginger, particularly, seems to help calm a lot of people's stomachs. I used it with great success when I was taking some very volatile-making medicine several years ago and recommend it highly. Peppermint tea also helps.
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