9 month old with Acid reflux

My daughter was diagnosed with Acid Reflux at 2 weeks old. She spent 4 months crying and spitting up half of her bottle and finally was prescribed Zantac. Now she is doing better but her food and bottle are still coming up her throat and she is swallowing it back down causing her to cough a little. I hear this mainly when is is moving around. Should I bring her to a specialist? or is this normal until she gets older? and is this damaging her throat? Her doctor just keeps increasing her dose of Zantac. I hate to put her through a bunch of test if her doctor is right. This is my first child and I need advice.