As alternative to baby reflux diagnosis, could you milk supply be 'fast'?
Read here on Kelly Mom about fast letdown
So dd was exactly how you describe: wasn't in pain (I didn't believe), was putting on weight beautifully and was generally happy. However, she would projectile vomit if she drank my milk quickly - and had to drink it quickly because it came out so quickly! She was just a 'sicky baby' which was messy and a pain in the arse.
I adjusted things as per that website advice which helped. The main thing I did was keep her upright for 5-10 min after a feed to let it go down and let her burb too.
We had occasions of projectile vomiting too - and literally loads would come up. Someone did say to me once, put milk in a egg cup and drop it on the side or tiled floor and it looks loads, so when the do throw up, dont be too alarmed as it probably isn't that much.
The other thing which combined the problem with dd was that she was a very 'sucky' baby. So she liked to comfort feed which I didn't have a problem with but it increased my supply, therefore she'd get a fast let down and more milk then needed - bit of a cycle. They say you can't over feed a breast fed baby - with dd you could
She'd just barf it up, and start again - not with any tears or upset mind. We therefore eventually got her to take a dummy and I was very strict when she had it (only straight after a feed to get her to stop feeding and when I knew she wasn't hungry or cluster feeding who was at certain times).
Speak to midwife or HV but it may not be reflux. Your baby would be screaming, be in pain and have other symptoms too.
Ps - congrats btw [happy]