Stop making excuses. Your are seriously underweight and should be aiming for *at least* 1kg of bodyweight gain per week. Your poor recovery explains the lifting progress.
>>> I really can't up my calories without my parents complaining where the food went
Flour, butter, nuts, nut butters, etc. are all calorically dense and cheap per calorie. You are trying to eat far too healthily. You are 16 years old and can eat garbage and grow... take advantage of that (while getting plenty of protein). All that fruit is filling you up... dump in a bunch of nuts and brown sugar instead. Use some oil or butter in your oatmeal. Stop eating chicken breast... eat thighs/legs (higher fat). Eat lots of pasta.