So, yes, at ~5,9 and 121lbs, that would indicate you're pretty slim - but I don't personally put much stock in BMI. Not knowing anything about your eating habits/background, I'd suggest that you don't need to lose fat, simply add some muscle to 'firm things up'.
1,100 really isn't all that much food, and could actually lead to physical damage if you keep your intake that low as a teen - your body is still growing/developing, and needs fuel to do it with! Eating too little is just as bad as eating too much, in terms of health and appearance. Aim for a MINIMUM of 0.8g of protein per kg of body weight (that's 45g/day, for you), up to 2.2g/kg (120g/day). Protein is important, especially while your body is still developing - it also helps to build muscle, which is what will add shape and replace what you describe as 'soft flab'.
I'd recommend bumping up your kcal to 1,800-2,000 (or more, if you can wrap your head around that) and adding at least 3 resistance training sessions (ie. weights!) a week to your schedule. Keep on with that for 6 weeks, and then reevaluate if you need to modify/tweak your workout and diet. Most basic calorie counters would put your 'maintenance' intake at ~2,000kcal, and you would actually need 200+/day more than that to put on muscle, so don't worry about eating too much - just so long as you're eating good food!
DO NOT add more workouts without increasing your food - and please, please, please do not drop your calories any further.
Beans, lentils, meat, fish, eggs, milk, LOTS OF VEGETABLES, some fruit, potatoes/yams, whole grains, etc. Enjoy your body, and enjoy your food - have fun!
General starter questions :)
