Dear S.,
The one thing about situations like this is that everyone gets so upset. I've got three boys, myself, and have been an in-home daycare provider for 24 years. Here's how I solve this problem when all else fails.
1. Sit on the floor with the medicine prepared.
2. Quickly place the child with his/her head at the apex of the "V" your thighs make to immobilize the child's head.
3. Put each of their arms under a thigh. (I don't know about you, but my thighs are soft enough that NO ONE is getting hurt...and it means you aren't battling flailing arms or a thrashing head.)
4. The child will normally protest. Who wouldn't?! But, once the mouth opens, place the dropper in the hinge of the jaw and gently squirt. This area is one that automatically causes a person to swallow.
5. Scoop up that baby and lay on the hugs, kisses, and "good jobs".
Viola! In 10 seconds you've administered the necessary medication and saved the child (and yourself) from a long-lasting battle.
Some folks will think I'm horrible...but medicine is a necessary evil and this method (again, when all else fails) allows you to get it over with and to move onto happier things almost immediately.