I wondered if it could be a medication being taken, but forgot to mention it... glad you thought to mention a drug!
If you are a teenager this is pretty normal lol. Low fat diets makes you hungry all the time. If you aren't drinking enough water the brain may think you are hungry not thirsty. Low stomach acid (hypochlorhydria) can cause unexplained hunger. If you are taking an drug then they may be causing an increase in appetite.
Rule out diabetes with polyphagia (lots of hunger)... the doctors like to use the Hg (aka Hb) A1c test nowadays to see what your blood sugar has been doing over a period of months.
Rule out a tapeworm getting some of your nutrition.
Rule out boredom, where you keep thinking of eating because you aren't focusing elsewhere enough.
Rule out hyperthyroidism, though weight gain doesn't typically happen with this overactive metabolizing problem with an overactive thyroid.
Rule out imbalance diet. I notice you don't mention an intake of fat, which is part of a balanced diet and is the source of the body's energy when the simple sugar, the carbs, and the protein have all been used up by your body.
You say you are allergic to wheat- do you have celiac disease -sprue where there's an absorption problem in the small intestine?
You are eating lots of healthy food which is good.
The reason you have gaind weight, is either you are eating too much fruit which contains fructose, too much fat or just miscalculating your calorie intake. It may be that you are now glucose intolerant.
If you are having too many calories and not burning them off, by moving and excerise, you will gain weight. Try drinking more water.
When I was at WeightWatchers, they used to say that sometimes when we feel hungry it is that we need water. If 10 minutes after drinking you still feel hungry then have something to eat.
You could see your doctor to check for glocose intolerance and also underactive thyroid gland.
An underactive gland slows the metabolism and hence weight gain.
It is very difficult to shift the weight.
Best wishes