My trainer suggested the HIIT/HIT training, as well, but it just does not agree with me. I, too, felt very nauseous and really did not want to continue to work out anymore if that was the way I was going to feel. I know that this type of training is the new "thing", but, frankly, I just went back to regular workouts and walking. I'm doing fine, feeling great and losing plenty of weight, so I think the good ole fashioned way sometimes works, too.
I think what you're eating looks fine, especially if you've tried different food groups before you work out and still feel rotten.
If it continues, I'd definitely talk to your trainer and try just the old way of working out, see if you're still nauseous.