This is a mild grade viral gastroenteritis (stomach flu). This subsides spontaneously in 4-5 days. Following would help you;
2) BRAT diet; banana, rice, applesauce, toast.
3) Soups, plenty of water, fresh fruit juices. Avoid bottled juices.
4) Avoid carbonated drinks.
Please feel free for your follow up questions.
In mild grade viral gastroenteritis; vomiting may be absent. The lack of solid stool is not worrisome as diarrhea would subside in next 1-2 days and stools would solidify, spontaneously. PeptoBismol can be taken, though. The mainstay of the treatment is prevention of dehydration. So adequate fluids, water, soups would be good enough to take care of it.
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