Reflux suffers do not generally sleep well (There are some exceptions and I really hope for your sake that the exception is your baby!). They struggle to self soothe and calm themselves into a deep sleep. They generally need your help in the form of feeding or some other crutch, like rocking or a dummy to get them to sleep.
On the matter of dummies - I found them to work for me. When a baby sucks a dummy he secretes additional saliva which helps to neutralise the stomach acid and this can ease the baby's discomfort. Dummies are especially useful for babies that comfort feed, as they will help to stretch the gaps between feeds and prevent over-feeding which often aggravates the situation. Having said that everyone from your Mother to the dentist has an opinion about Dummies so do what works for you! It took me 8 months to get my little one to take a dummy and after that, it really helped her to self soothe. You are either a Dummy Mom or not. And just remember there are very few adults walking around with a Dummy - so the habit is fairly easy to kick. Do anything to save yourself a few more grey hairs and hours of rocking- which can be back breaking!
Reflux babies tend to take very short naps during the day. It can nearly destroy you to rock, calm and settle your baby for about an hour, and when she eventually falls asleep you leopard crawl out the room so as not to disturb the light sleeper! And then, not even 5 minutes later, you go cold at the sound of a blood curdling scream and she is awake again.(My little one would wake at the sound of bare feet on the carpet!! I then introduced a little blow fan (white noise) and that has significantly improved the depth of her sleep. A Classical music CD or Toy has the similar effect, and can be great at blocking out household noise.
The other problem we experienced in the early days, was putting her down into her cot. We would rock and bounce her on a ball (subsequent research suggests this is NOT a good idea, as it can worsen the Reflux!! You live and learn!!) and the second we put her down, her eyes would shoot open and the cries would start. It was as if the sheets were electrically charged and shocked her as we put her down. We would then pick her up and start again. It could sometimes take up to 15 attempts to finally get her to sleep. I even tried rocking her on a pillow and then placing her down on the pillow, in case it was the cold sheets that were waking her up! I have since read some very good advice, do what works for you, to get both of you some sleep. If it means the baby sleeps on your chest and you can also sleep then by all means do that! Just be very careful in terms of sleep safety, to prevent any harm coming to your baby.
I made three very brave attempts at teaching her to put herself to sleep (sleep training), and all failed (well not exactly failed, but certainly did not make ground breaking improvements after a very long time. I must have hung over that cot for over a week in hours!). She would lie there, not cry, but just lie there for about an hour before falling asleep, and it quite frankly nearly destroyed me! My suggestion would be to do what works for you. I fed mine to sleep – not exactly what the experts advise – but it worked for me. Remember those who say don't do it are not sitting with you every night helping with a screaming baby, and they most likely have never had a Reflux baby! Night wakings are also often very frequent. At the worst stage I was getting up every half hour to hour at night to a screaming baby who would not be calmed, except by feeding which just aggravated the situation. I found that her worst stage was at about 8 months, well after the time the experts suggest it should have reached its peak. As I mentioned before every child is different.
My suggestion would be, not to do what I did- as I think I created bad sleeping habits which I am still paying for, but to seek help from an expert in the field, contact a Sleep and Routine Specialist and they will be able to advise you on the best approach to teach your baby to sleep, and for you to get some much needed sleep too. It will be worth every cent!!