I'm sorry but I have to disagree with your doc. A 3 wk old doesn't need water. In the past (way in the past) formula was not so well balanced as it is now and there could understandably be instances where LO might need some water but modern formulas are very well balanced and a LO really shouldn't be taking water at this age.
Reflux doesn't always involve huge amounts of sick, silent reflux is painful and damaging and often shows very very little or no sick up. There are lots of FAQs on this board:
Colic, Reflux, & Cryingyou can also read symptoms of reflux and silent reflux here
http://www.cradle2kindy.com.au/BlogRetrieve.aspx?BlogID=1159&PostID=15358I'd probably start with this page just to see the list of symptoms before exploring the BW reflux boards further, after all you don't know yet if this might be the cause of the excessive feeding to the point of sickness. If you don't have time to read the whole page just scroll down to the symptoms list.
If you feel that your LO might have reflux or silent reflux tell your GP you want a referral to a paediatrician. GP's cannot be expected to know everything about everything. If it is reflux you need reflux formula or a safe thickener that can be added to your regular formula, and meds to control the acid. I still wouldn't use hungry baby milk.
Don't worry about going back to the GP to ask for a referral, it is your LO's health that is the most important thing. I know it can be hard to be assertive. xx
Are you giving him enough milk in his bottle so that he takes to his fill and there is still some milk left (about 30ml or 1oz)? LOs should be offered more than they take so you know they are full. This might help reduce the frequent feeds. You can also try stopping to burp half way through the feed in case he has wind filling his tummy, not leaving enough space for the milk.
Waffling3 - just want to say that there are good reflux meds available to control stomach acid if LO needs them. Infant Gaviscon was an ok temporary measure for us but isn't viewed particularly highly as a long term solution. The damage caused by reflux can be considerable so LOs should be properly medicated where necessary, holding out to weaning isn't always the answer. My DS is 21 months, been eating solids since 6 months and still has reflux meds twice daily plus a thickener in his large milk drink of the day (he can manage an oz or 2 of milk without thickener as a drink with his dinner). There is a list of the possible results of untreated reflux in that link above if you wanted to take a look. xx