You'll have to wait and see what happens. If she gets her period, breath a sigh of relief, and learn from this mistake. If she doesn't, wait a week and then try a pregnancy test.
You don't mention if she's missed her period, you only state that she's vomiting. Yes, she could be feeling symptoms of pregnancy if she became pregnant on July 5, but vomiting alone isn't an accurate symptom of pregnancy. Vomiting can happen for many other reasons.
Fact is, any time you have sex, even if you use protection, pregnancy is possible. The fact that you didn't use protection increases the odds. Now you have to do what everyone else does when they think a pregnancy has occurred. You have to wait, and then test.
Good luck.
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