Living in Texas, you only have one option, Texas A&M University for veterinary education. Of course, there are more in other states, including (relatively near) Colorado, California, and Louisiana.
First, check out the website for the American Veterinary Medical Association. They will have answers to many of your questions. Also, once check the individual colleges, or at least those you are interested in. They may have different pre-requisites that you may need to complete.
Many universities want the science courses to be fairly recent, so be prepared to go back to school and retake (or take for the first time) courses like biology, chemistry, physics, organic chemistry, biochemistry, genetics, calculus, other zoology and animal science (husbandry) courses, etc.
The standarized test used for vet school application is the GRE, although the MCAT can also be used. There was a test called the VCAT, but only two universities required it, and it is no longer offered. From what I remember, GRE scores cannot be more than 5 years old.
Also, and this is important, probably more important than visiting AVMA (or up there)… try to find a volunteer job working around animals. A veterinary clinic, animal hospital, animal shelter, zoo, perhaps even a research lab. I’ve met people who wanted to become veterinarians… until they saw their first surgery and saw the work involved in becoming a veterinarian, since it is not only about taking care of fluffy cute animals. Since you like avian medicine, try finding an exotics or wildlife rehab clinic.
The four years of veterinary medicine school prepare you to become a general veterinarian that can work with different species. You may take some electives during those years that can help you especialize a bit in a particular area. Internships and residencies are not required upon graduation, but they are needed if you want to especialize in a particular area. Internships are 1 year deals, residencies vary 2-3 and usually combine with a master’s or Ph.D. program. You do not need to have an internship before going to residency.
I think it is good you’re interested in avian medicine, not a lot of people go into that area, so saying that in the application by the time you’re going to apply may make universities more interested in knowing more about you.
Since you need to (re)take college courses (1-2 years if you start now), plus study for GRE or MCAT, then the 4 years of vet school (assuming you get in after your first try, only 30% of those who apply are admitted somewhere), then 1-3 years of specialization… It’ll take you about 6 years to become a veterinarian.
Oh yea… schools like Cornell and UC-Davis are highly spoken, but they’re also really hard to get into (well, harder than average). Almost all the vet schools are public, so they tend to favor in-state residents (they’re less selective with them than with out of state students). The AVMA has a list of accredited schools in the US, Canada, UK, New Zealand, Australia, and the Caribbean. Frankly, any one of those are good schools to attend. For the foreign countries, what happens is that you do part of your rotations (3 or 4th year) in the US.