I had the same problem too. When you tell your freind, you dont have to go into depth about it but the best way to tell her is to open up with:
"I'm guessing you've noticed that I can get a bit nervy in some situations like when we're out (Add an example, whether it be, excessive hand washing, or whatever it is you do that she may have noticed) but i'm getting fed up with making excuses about it, I have a big phobia of vomit and it effects alot of things in my life, I feel comfortable telling you and I want you to know about it so I dont have to make up excuses anymore" You dont have to say that word for word but you get the idea I hope, add in anything you want and like the comment above me says, just tell her how it makes you feel.

Also, the more you learn about emetophobia the more you understand it and it becomes easier to explain to people what it is and talking to other sufferers really helps you to talk about it and feel less shy because it's a great feeling to know you're not the only one, that's what I've found anyway.
I totally understand that you don't wanna tell other people and feel embarresed, people aren't always as understanding :/ i've only told those closest to me.

Hope it all goes okay, i'm sure she'll be there for you