I'm in shock. You just described my reaction to broccoli to a T. I've never met or spoken with anyone who reacts to it as violently as I do. People usually don't believe me so I don't talk about it much and just push the broccoli aside.
The only explanation I've found is I'm sensitive to salicylates. Weirdly, I do not react to all foods and products that contain salicylates, but I've found that broccoli is by far the worst. Others sometimes give me a hint of feeling ill, but nothing that makes me totally averse to them. Maybe you have this sensitivity too? Here's a little more info. ht