Hi Kate
I can only tell you about my experiences as I'm no expert. When I first began exercising I felt very sick afterwards, and the head-spins were shocking too!!! I don't personally feel it's to do with the food so much as exercising too vigorously. I hear you... 'I *have* to exercise vigorously or how will I improve?'
These days I'm fairly fit and it doesn't seem to matter what I have to eat beforehand. If I'm going to be exercising immediately afterwards then I have a light fruit breakfast or fruit juice - that's my choice, and works well for me.
Someone who *is* an expert in the field once advised me that I should finish every training session feeling as if I could do more. Seemed counter-productive, but my fitness has increased very steadily as a result of this practice so I'm a won convert. His other piece of advice was to eat some fruit immediately after training as this prevents muscle soreness, also spot on and great advice. However, you can't do that if you're throwing up!
Have you told your PT that this is happening? Please do if you haven't already!!! S/he needs to know as I believe it has a lot to do with your blood-pressure and that's their job to watch that.
Yes, I have told gym staff that I eat raw. They open and close their mouths a few times, ask a couple of bewildered questions, but as soon as I give informed answers they have just replied "Oh well, I guess you know what you're doing, but be careful". I've very generously not replied with the same comment to them!!!
I used to get dizzy and wobbly if I didn't eat soon after waking up, or for extended periods during the day. Thankfully this has gone now but I think it's to do with blood-sugar levels. Maybe have a look at making sure you have plenty of low GI foods in your diet? Though on raw you'd be hard pushed not to! Fruit digests a lot faster than fatty foods, I wonder if that has any impact on the way you feel? But I truly think it's the exercise being overly strenuous and not the food's fault at all.
I hope that helps you Kate

And that these awful reactions stop sooner rather than later.
Much love
CareBear