I too was air sick on my first ever trial lesson, although I never got any carrots and peas up! Never had it since.
What causes it is the fluid in your otoliths (the tubes in your ear which tell you which way up you are) Normally it is due to movement about the three axis and worsened by lack of input from the eyes confirming what the ear is telling your brain; like sitting in the passenger cabin looking out f the side window whilst in cloud as we pull lots of 'G' up front!
Have you ever sat in a car and read a book? This can give you the same effect, especially on a twisty A road and especially if you keep moving your head about too. This is why people who get car sick tend to get it in the back, but not so much in the front (a better view giving them an horizon to focus on), again exacerbated in kids who tend to sit lower down and don't get a full view out of the side windows in certain cars.
When flying GA, if you get it, try to fly straight and level and stop moving your head around. If you do not already have control, handling can help to alleviate it (not sure how it works, perhaps it gets you doing something and stops you thinking about it). I have not flown with any commercial pilots who get it, I think the view out of an airliner around virtually 270 degrees of sky can help, as does the instrument presentation. I have never had it since my first time up, but it concerned me at that point as to whether I'd be able to cope if I was going to feel like that every time. What I don't think helped then was the instructor was demonstrating the effects of controls when you experience yawing, which is not a usual movement for a land lubber to have felt before!
Hope that helps.
PP