asthma - 7 y.o.

My son has asthma since 6 months old. He's easily triggered by environmental allergies. He coughs whenever he's at school or at the gym. It was worse in the past when he could not go to the mall or the library. He was treated with NAET but we've seem to hit a wall. We also went to a homeopath for 1.5 years with no improvement at all. I'm hoping someone might be able to offer some advice.

He has lots of food allergies: gluten, dairy, corn, pepper, oily foods (eg. pork)

Fully Vaccinated till 5 y.o.

History:
Had severe eczema from head to toe since 3 months. Chinese herbs cleared most of it at 1 y.o. Now, eczema patches on limbs.

Asthma type: coughing continuously and wheezing. Wet cough.

Worse when : cold weather, oily foods, at places like school/gym (environmental trigger), eat the offending foods

Better when : warm weather

He doesn't like to drink or sleep. Has to be reminded to do both.

If asthma left untreated with inhalers, he would cough / wheeze till he doubles over and has to lie down.

He's slim. Short for his age.

Other : Grinds teeth in his sleep. Has speech delay. Doesn't know how to convey his thoughts through words. Loves to draw. Nosebleeds usu. comes on during sleep or when he coughs a lot (inhalers do not work on the first 2 days of a cold).