Claire, our stories sound identical! The dr's scared us with the pyloric stenosis, but it was unfounded and no one even thought to suggest reflux.
I realize now and much too late that my son had reflux. But as Sharon mentioned, you may just have a spitter. I found things that comforted my son was being in an upright position and not putting on his tummy after feeding. My son would throw up entire feeds sometimes 3 times a day, but he still gained weight. It may make you feel better to know that breastmilk is absorbed very quickly... the nutrients and good stuff I mean. So although the feed is not staying down, they are still getting what they need.
Also, try little burps every couple minutes and see if this maybe helps... (it didn't for us)
Or one mom started skipping burps all together.
I hope this helps.