I’m not either but I do know someone that was going to school to become a vet. It’s very competitive and she told me it would have been easier to get in to med school.
Here’s some info on Vet education requirements from the Department of Labor.
http://www.bls.gov/ooh/healthcare/veterinarians.htm#tab-4
According the that info there are 28 schools with Vet programs in the US. Less than half of all applicants get into veterinary programs. Most people have a Bachelor’s before they apply to a vet program so collectively you’re looking at a total of 8 years in college.
I found this info on the education required to be a dentist:
http://education-portal.com/education_needed_to_become_a_dentist.html
It takes just about as long education wise. 4 years for a bachelors and then 4 more for dental school, 8 total. You have to pass the Dental Admissions Test (DAT) before you can apply to dental school.
Both careers are attainable if you put in the hard work and prepare for them. I do think that trying to do BOTH would be a little unrealistic. Either would be a full time job and require a lot of dedication, ongoing training, etc… I’m definitely not trying to discourage you. You have a lot of time to figure out what you want to do 