Put the med in a syringe. The kind that you are able to work with one hand, even the type this is like an huge eye dropper. Put the med aside, maybe in the front of a drawer.
Take your daughter and lay her down on top of a dresser or something about waist high to you, the med should be within reach of your right hand. Take a blanket and wrap her up burrito style. I am right handed so this is how "I" do this.
I put my left arm around the head, laying it on the dresser top. Then I use it to hold the head straight and use the fingers to help open the mouth and more. She's going to be kicking and screaming but this is good. She'll have her mouth open and be swallowing a lot.
Use your right arm to go across her rib cage and hold her down. Use your right hand to hold the dropper/syringe. Use your left hand and right hands together to get her mouth open. Put the dropper/syringe in her mouth. She may bite it or try to push it out. Don't hurt her of course but squeeze a couple of drops into the back side of her mouth. I try for the space between the jaw teeth and the jowl. This is soft tissue and she can't spit it out so quickly.
Then just keep going back in and putting a couple more drops in. She'll get some down.
IF you do this a couple of times she's going to know what's coming and she'll fight you even more. Stay calm and look her straight in the eyes and say
"Why does mommy have to do the medicine this way?" She will say stuff not right. Then say "Mommy has to do meds this way because you have to take them. Dr. XXX said if you don't take this med you have to go to the doc's office and get the med in shots because you have to have the meds. We are going to do the med like Dr. XXX says. Would you like to take the med in your mouth and swallow it without being a burrito?"
If she says she wants it in a shot instead load her up and go towards the doc's office. If she asks where you're going tell her it's time for her meds so you're heading to the doc's office to get the shot. She should totally freak at this if she's a normal 3 year old. They usually hate shots.
You will be, in effect, teaching her to conform and decide she wants to take the meds because you giving her the med is so much worse.
We had to do this a few rounds of meds then our little guy was totally ready to take meds no matter how disgusting it was. That white antibiotic is the nastiest stuff....