I'm 100% sure you'll be fine, you took excellent preventative measures and were only near her for a few seconds. The two hour thing isn't true, and you used a sleeve to open the door.

I do have to say though, please don't starve yourself. I am 15 and I've been dealing with this phobia since I was 6. Over the years I've found that I feel so much worse when I don't eat anything (If you don't feel like eating, get something like cream of wheat, which is INCREDIBLY gentle) and so much better if I do. Also, I did get sick for the first time in years a little while ago, and I can say with absolute certainty, getting sick with something in your stomach is so much better than on an empty stomach. Much less painful.