So, some kids do not tolerate antibiotics and antacids probably would not help. One of my sons had a terrible time in the toddler years taking liquid antibiotics which I assume you are referring to. SOOO much better once he was old enough to take pills. There are some antibiotics that come in chewables that might be an option (augment is one).
If you are wanting her to be diagnosed with true Gerd, I'd wait until she is clear of these other things going on and begin tracking symptoms.
As to avoiding throwing up, instead of the dropper -- try giving it on a spoon the way food is given. Or use the dropper but squirt into the side of cheek rather than down the throat. Ask for flavorings when you pick it up at pharmacy as they can add those which help. Taking the antibiotic with a meal and/or a glass of water can help as well.
If you feel she is not tolerating the antibiotic and throwing it up because of that, talk to the doctor as there may be a different antibiotic choice.
It's rough when kids are sick. And especially if we think the medicine to get better is contributing to making them feel bad. good luck