Francis,
As the mother of both a "normal" and disabled child, as well as someone who has worked with the disabled, I know the feeling. A baby will not choke to death on that little bit of medicine. The best way, I found, is to put the dropper in the side of the mouth, between the cheek and gum. The medicine just hit the back of the throat at the wrong time and she gagged, which scared her and she may actually have been holding her breath on her own or out of reflex. When you put it in the cheek, it does not suddenly hit the back of the throat where the gag reflex is the strongest. Just give her a little at a time.
I agree with the others on the Infant CPR class. They will not only teach you how to do CPR on a baby, but how to handle choking as well. Many children have at least one episode of choking on food before they are grown, and you need to know how to handle it so you don't panic or do the wrong thing.
Both you and your baby, I am sure, will be just fine.