Cough along with more than 24hrs of vomiting

Good day Doc, I have a 5-year-old kid who has been prone to catching colds, so last week she had some thick mucus coming from her nose with only dry cough for a few days, then on the early morning of 7th day she was feeling nauseous and that's when the constant vomiting started. She was vomiting the whole day, with an interval of 15 - 20 minutes or whenever she coughs it somehow triggers her to vomit. Note that her vomit has phlegm in it, there was no fever nor diarrhea, however, her stomach was aching. The next day, her vomiting stopped during the day, however at night she vomited twice. Although she's prone to catching colds but she rarely vomits like this, last time she had constant vomiting and diarrhea was when she was 3yo. I gave her Pedialyte drink, over-the-counter medications and did home remedies in hopes that she would get better. I am trying to understand here is how does this happens? What would be its diagnosis?