My daughter vomited right after taking her medicine (she was crying so hard that she ended up upsetting her tummy). Does this mean I have to repeat the dose?

Give it a 15 to 30-minute interval and see if she throws up again. You can gauge it if your child's tummy is a bit better already. If your child already know how talk, you can ask how she's feeling and you can gauge if she's ready to take in the medicine.