height to weight?

i'm 5 foot 2 and i weigh 114 and most websites tell me that's healthy if not, almost underweight but i feel way too fat and i'm not just saying that for attention so please no comments like "if you're fat i'm obese!!!!" i'm genuinely wondering if it would be bad for me to lose weight? 
would running a mile or 2 a day and eating less junk food help?