Food poisoning can pass on its own. In fact, most cases of foodborne illnesses pass on their own. However, in the meantime, they suck to have. They typically present as vomiting and diarrhea for a couple of days. Stool can remain looser than normal for up to a week after it passes. In some more serious cases, you might get a fever and the joys that come with that - hot flashes, chills, sweats, and the general achiness of a cold.
There are times when you will want to get a doctor’s opinion. Generally, any time you are worried about your symptoms, you should see a doctor. Any fever that lasts more than two days is a good reason to go, especially if you’re vomiting and have diarrhea for the entire time.