Thats Brill news Sarah, I too dont think you could have done anymore, and I prob would have paniced and not even stuck hand down throat ??? who knows its one of those things you dont know till you in the situation!
is there anywhere that does a doggie first aid near you? A creche near us does one a few times a year 2 hours and it just the basics bandage cuts bites etc – and they have calm dogs to practise on, but would give the confidence to know there is no more you could have done.