You are not fat at all. Quite the opposite really, but your situation is not an isolated incident, as I know plenty of other folks who are healthy but think that they're fat. You want fat, I'm 21 standing at around 6 feet even and tipping the scales at 230 lbs with little muscle mass. Granted I'm a guy writing this, but it puts things in perspective. Being in the 5'4 range and weighing under 100 lbs is normal.
I don't know you, but I can tell that you're a beautiful young lady and you have nothing to be ashamed of, I assure you.