For some reason whenever I see blood in surgery, especially if I haven't seen a surgery in a while, my body decides that it's nap time
I've come close many, many times to fainting, and I actually passed out once in front of a bunch of fourth years and vets when I was pre-vet (so embarrassing!) BUT it's just something you have to get used to.
For some reason some people (like myself) just react that way. It doesn't make sense - I'm not afraid of blood. In fact, I think surgery is hella cool! If you end up being like me, though, don't worry! Everyone has always been super understanding and very accommodating with me. Over the years I've just gotten used to it where it hardly ever affects me anymore.
Some tips if you do end up queasy: I've found that my queasiness levels are much worse if I skip breakfast. So, that's a no-no. I would bring granola bars with me when I shadowed so I could get my sugar levels up before watching a surgery (not sure if it actually helped, but I felt like it did). I also found that sitting on a stool during the procedure and asking the doctor as many questions as I could think of really helped me keep my mind off of it, too. If you start feeling hot, clammy, and light-headed just let whoever you're with know you've got to go sit down (cold tile floors feel the best!). It's better than fainting onto the surgery table
If it persists, you need to make sure you're up front about it, and whoever you're shadowing SHOULD understand.
But really, it's normal to be nervous. When I was in high school, the whole thing kind of freaked me out, too, but now I'm really excited to learn how to do all of it! Shadowing a vet will definitely help you learn if you're choosing the right profession
And if you still want to be a vet but don't want to do surgeries, like others have said, you do have other options. Good luck!