I have been through this. My first son had acid reflux - bad. And my friend just had a baby 3 months ago and he has it so it's fresh in my mind.
I was nursing so it would take me forever to feed him (you know how hard it is to feed a newborn, he'd fall asleep everytime he got near me!), then when I finally got him to eat, he'd throw it all up! I was a mess. I thought my baby was starving. But he wasn't. He kept gaining weight, so the doctor said he okay and he was. As long as he/she gains weight, he's/she's getting food.
We got through it and my son is now 4 1/2 and doing great! And your daughter will be okay too! Here's my advice:
1) I am very surprised your doctor said to stop nursing. My doctor would never tell me that. Instead I had to endure the brunt of it. The doctor put me on a strict diet (no beef, no soy, no dairy) because those are typically what bothers babies with reflux. I lost all my baby weight and it helped curb my babies acid reflux, so it was a win - win situation.
2) They also put my son on prevacid. I wasn't happy about putting a newborn on medication and I'd cry about it all the time but I didn't know what else to do. He took it for 6 months then we slowly weened him off.
3) When he was approaching 4 months they told me to add a little rice cereal to each bottle, just a tablespoon or so.
And when he was 4 months they said it was okay to give him a little rice cereal each day. Then at 6 months, it was full blown solid baby food. I would start with veggies as they are less acidic.
4) I rarely laid him flat. Accept for tummy time when he got older.
Only hours after eating would he lay flat to play (when he got old enough to play). As a newborn he was always angled, even if it was slightly.
When he was a newborn I'd put blankets under his upper body (like when we were in the living room during the day). In his bassinets under his sheet I'd put blankets too so he was angled.
When he hit about 4 months and could sit in those bouncers things, he was always in that or his swing (again when were in the living room during the day). NEVER FLAT.
When he was 6 months, he could sit up so during the day wasn't a big deal. And at night in his crib, I bought a wedge of foam and put it on his bed and used a blanket over the sheet to hold it in place.
When they are angled all the time, yes, he'd slip down and be lying funny so I'd have to get up and check on him throughout the night to reposition him (but what parent doesn't get up and check on their little ones? right?). That's the kind of stuff of mom's have to do. :)
If I can think of anything else, I will write you again.
Best of luck. Hang in there. :)