I was born with numerous anxiety disorders. Once my epilepsy developed (particularly because it's localized in the temporal lobe), that anxiety became exacerbated. Moreover, my medication caused me cognitive impairment, starting my senior year of high school. My dosage finally decreased recently, and my grades are noticeably higher. Unfortunately, because I applied this year, vet schools weren't able to see the extent the medicine affected my cognition, and as a result, I got rejected from a few schools, due to my numbers. Still, some gave me a chance (with interviews), though I'm still in the waiting game (and I'm not going to lie - the waiting, along with my anxiety, really sucks, but you can learn how to cope).
How did I cope during most of college? I didn't, and as a result, I developed disordered eating. It's one of the worst things I ever did to myself, and it could be prevented. How did I cope more recently, during the application process? By going to therapy once a week. I've learned so much about myself during this journey, which made it much easier. When my medicine can't calm me down (like during panic attacks), I take a walk and listen to my iPod, and I try doing guided meditations on Youtube.
Anxiety and it's effects can be crippling. You can't avoid it, but you can adapt. Some schools weren't able to give my a chance, and I'm not surprised by that, but others were. If this is what you really want to do, just keep dedicating yourself. Life becomes much easier when you realize that you have a passion, because then you have a purpose; you can live towards something. If you're in this for the animals, just remember: they don't care what school you go to, how many tries it took, and how twisted your journey was; they only want to be taken care of.
The best piece of advice I can give you during this journey (which I learned from Demi Lovato actually) is that the energy you put into the universe will be returned to you. You can let you're anxiety overwhelm you and emit negative energy to your world, and in turn, your life will be a mess; but it doesn't have to be. You can emit positive energy and remember that not ever obstacle is the worst thing in the world. Having severe anxiety makes this all the more hard, but it's not impossible. It's up to you.
Best of luck! 🙂