Yup, sounds like me. There are, however, several years between now and being a graduated, licensed veterinarian to think it over (and just get over the squeamishness). I'm reliably told that all emergency workers vomit the first time, and everybody vomits for the first human autopsy, or the first murder scene, too. It's normal to be squeamish, but eventually, what made you squeamish becomes the new normal. I'm still not over it, but it's becoming more normal and less squeamish. In another decade, I'll probably be fine with dissections and needles and howling puppies and blood and gore and guts. I'm still nauseated during dissections, but it's becoming less an issue of the subject and more just a smell thing. The chemicals used in preserving specimens for dissection just reek like crazy. Not that dissections are the most appetizing of experiences, of course.
Blood would always make me weak in the knees and elbows. I'd get lightheaded, feel super nauseous, take hours to recover, that sort of thing. But I'm better about it now, and recovery doesn't take as long anymore. It'll get easier, and then, why, you'll feel like a bad mammajamma then!
Worst case, you'd make a kick butt science teacher.