As L. as she's gaining weight and isn't obviously uncomfortable, there really isn't much any dr will do. There are also two kinds of reflux. There is reflux, which is simply that the digestive system is still maturing and trying to work things out. That kind of reflux is not effected by medications. Then there is acid reflux, which my son has a severe case of. Acid reflux is painful and often causes weight loss and is treated with medications.
As I said, Cody has severe acid reflux. He is on two medications for it (Prevacid to prevent damage from the acid coming up and Reglan to aid in his stomach emptying faster to try to prevent the vomitting - he vomits entire feedings). I did exclusively breastfeed for 10 wks but had to stop because of his reflux. After a trip to the ER and an overnight stay, it was determined that the best thing for him was thickened feedings. Since I obviously can't add rice cereal into my boobs, I had to stop breastfeeding.
Cody drinks Enfamil Lipil and we add rice cereal to his bottles (this is only recommended if recommended by a doctor). He actually gets 3 tbs of cereal in a 4 oz bottle, which is way thicker than most babies would get.
Enfamil makes a formula for babies that is already thickened, called Enfamil AR (added rice). It is a great option, but simply wasn't thick enough for my son.
You said your daughter is 4 months, have you tried feeding cereal or oatmeal from the spoon? Our pediatrician gave us the go-ahead when Cody was 4 months and it helped a lot. At 5 months he started baby foods. He never vomits any of the food, just the bottles.