I had the Heimlich done on me once and it saved my life - and I have done it twice on others. It is simple and effective.
Dont be afraid - if someone is really choking(not just coughing, hacking - you will know by the lack of ability to inhale) - just let it rip. I actually broke my dads rib when I did it to him - he was old and a little frail - but hey - he was alive.
Nice job with the dog - my wife took doggy cpr lessons a few years ago. Yup - they have doggy cpr classes. Its not as easy as a person - lol!!