What does it mean when I feel that I have to "work off" every bit of food that I eat?

No need to panic, but it might mean that you're being too hard on yourself. Remember that food is there to nurture us and keep our bodies going, there is nothing wrong with calories, and you shouldn't punish yourself for eating! Be good to yourself instead and eat a variety of food, fresh ingredients, try new recipes, enjoy take away now and then. Exercise everyday, but do things you like without counting how many calories you burn, and don't overdo it, because fatigue causes burnout sooner or later. Keep in mind that moderation is key both in fitness and nutrition!