Hi MyDaydream, I had exactly the same thing with my DS, at about the same age. A rash (that did seem to distress him as he scratched it quite vigourously) but no other ill effects. I was concerned since I wasn't sure if the next time it could be worse.
My short advice would be to go to your GP, but that they'll probably just advise what you've suggested in your post.
Long advice is I went to the GP who told me that there was no such thing as an anaphylactic reaction to egg (NOT true!) and sent me on my way.
I went back, saw another GP who said that she'd just been to an alergy seminar and that it's quite possible to have a skin reaction but nothing internal and that I should avoid giving any egg for a few months. I could then try again (with some prescribed piriton at the ready), or I could come back to the GP and they would refer me to the allergy clinic at the hospital.
My DS is now nearly 10 months and I haven't tried egg on its own (eg scrambled) yet. But I realise I've given him things that contain egg, like egg pasta, yorkshire puddings and cake. I think I'll try giving scrambled egg again in the next few weeks and see what happens, and if he reacts again then I'll get along to the allergy clinic.
Sorry, that was a bit of a ramble about me... hope it helped anyway.