Ah, I am in Vancouver so that's a little far to meet up for a doggie walk, nevermind then!
Well my heart goes out to you, I am a nervous nellie at heart and I understand how you feel. If it gets much worse it may not be a bad idea to see someone about (not a GP, see a psychologist or psychiatrist), even for just a few sessions to learn how to manage those feelings. A lot of the skills they can teach you via cognitive behavioural therapy can be applied to future situations where you may feel anxiety, as well.
I am also very close to my parents and I think you are very brave to move away! One way of looking at it is imagine it as an adventure. Nothing is set in stone, so if you are really unhappy there, you can move back
You are moving to a brand new place and starting a life there with Tyler - that's exciting!
Also, get your parents Skype on their computer before you go. Free, face to face chats... Next best thing to seeing each other in person.
*hugs* You are strong, and you are going to make it