After eating a small meal of apple, carrots, light low calorie bread, and one piece of fake meat. i fell asleep 30 minutes later for a half an hour or so. weill i gain weight or will i be ok?

You should be fine: Whether you gain weight or not is a balance between how much you take in and how much you lose by exercise, etc. It is not uncommon to be sleepy after eating, particularly after lunch.

You will be ok: No this much consumption of carrot and low cal bread and a fake piece will not make you gain any significant weight.You have to consume 3500 calories extra without any activity , more than your body needs to maintain your normal weight to gain 1 lb of weight. So at your age if you have normal range weight and bmi you do not have to worry about weight after consuming few calories and sleeping.