They sound exactly like the asthma attacks my son used to get, set off by colds or allergies. His started at 5 years and he was diagnosed at 8 after a few collapses and going blue. Also, you could see his sides being sucked in under his ribs. Touch wood, he hasn't had an attack since the preventer inhalers have been increased. If it is asthma, the inhalers used correctly (with spacer) will help. Have they tried oral prednisolone? Does a nebuliser help?
They used to diagnose asthma from a year and bronchiolitis before that, so that's changed in the last few years.