Am I going through a growth spurt?

Yes, you are going through a growth spurt. Everybody does during adolescence, and the amount you grow and the rate at which you grow has little to do with what you eat. Most girls get as tall as they're going to get by the time they get to be 18 years old, give or take a year or two. Now, the fact that you're feeling sick also has little to do with your growth spurt. Perhaps it's your first period developing, or perhaps you've got indigestion from eating too many different kinds of food at once, or perhaps some of the food you ate had food poisoning. At all events, see your doctor right away. If your bloat, warmth, and heart rate are due to nothing more than your menstrual cycle developing, it's better to be sure than sorry later.