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Morning sickness and vomitings are generally thought to be associated with pregnancy . In your case after having sex 3 days back , if vomitings and nausea occurs then it is unlikely to be due to pregnancy as the nausea is caused by the increased beta hcg levels in the blood following fertilisation and implantation and it takes time.
However the best way to rule out pregnancy now, would be to get blood serum beta hcg levels done, if they show raised levels then you are likely to be pregnant.
I hope i have answered your query in detail,
wishing you good health ,
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