If your school’s counseling service is too busy to be of help, and you have health insurance, see a private therapist or counselor. Do that as your first priority, no matter where you go for the summer or how long you think you’ll spend there. As you said, it’s impossible to know how you might feel about things if you were healthy; so make it your priority to get your health in order. Start that today - find out which counselors are on your medical insurance in the town where you’ll be living this summer, and contact them for an appointment for once you get there.
I would suggest that you consider taking at least one term off from school while you figure out your next steps, perhaps even two. That’s because right now, with your GPA, you are an extreme long shot for vet school. However, if you can come back to school and from that point on do very, very well (3.5 or higher each term from this point forward), this is an entirely different story re: vet school. But there needs to be a clear break, a defined before (so-so grades) and after (great grades) for this to work. And you need enough time in school after the great grades start for them to be meaningful. If you can get some help with your health and return to school strong in the fall, that’s fine. But if you think one summer isn’t enough time to do that, then be wise and take a term off.
It should be possible for you to get a leave of absence from your current school, if you decide to take time off. This holds your place at your current school, and buys you time to get your health in order, and to look at the other schools that interest you.