Oh Have Hope, I feel for you. Something similar happened to me recently, but instead of staying away and hiding (like I want to) I will go back and act confident: hold my head high, greet others with a nice 'hello' and continue on my way keeping to myself and being as effective as possible. I'm not going to apologize or cower, I'll have my shoulders back and make eye contact, but I won't stick my neck out for things... just keep going.

One thing is likely: that your feelings and preoccupation with the meeting is a lot bigger in your mind than in anyone else's...

Keep going...!!! With time your feelings of shame will lessen...