Thank you for posting your question here, I will try to answer it to the best of my abilities.
Yeah, it seems like you do have a case of food poisoning
, in most cases it relives itself and is nothing to worry about. I do recommend you drink a lot of fluids to avoid getting dehydrated.
If your condition doesnt improve in a few hours and you feel just as bad the next day, then go see a doctor. But in all likelihood you should be okay by then.
I hope this answered your question.