Travelling
If a skater travels while doing a fast spin, it will create dizziness and inner ear/vestibular dysconjugate activities. This can release certain chemicals in the brain stem, which will irritate/excite the vomitting center (the "area postrema" of the brain) and you will feel like puking.
My advice---until you completely master centering spins, do not try two in a row. Try a combination spin instead, like sit-scratch spin, or camel-sit spin, or sit-change-sit.
In lieu of this, you can get your "motion sickness" to lighten up a bit if you focus on the top of the boards while spinning (DON'T LOOK DOWN!! YOU WILL GET DIZZY!).
So, to avoid your motion sickness from spinning:
a) Please center your spins.
b) Please don't look down in your spins or their exit edges.
c) Please, focus on the top of the boards, like a horizon as you exit your spin.
d) Please don't rush into your second spin, ride that left forward outside edge before getting into your spin position (if you skate counter clockwise like most) while looking at your "horizon".
Rushing your technique will cause travelling, slow spins that wobble and a poor transition betweek spins.
Building up from starting the spins slowly, well centered, and then adding power and speed to them as you improve will also help you avoid this problem, as you will be training you brain /inner ears and body in the process.
GOOD LUCK! You sound like a great student to your coach.