six ounces seems like it might be too much for a three week old, so that
might have caused the projectile vomiting, especially if she was eating too fast. definitely make sure she is eating with a slow flow nipple, and as someone else mentioned, try burping her more often. if you're already burping after each ounce, then do half ounces.... it's a pain, but it's less of a pain than having to change her clothes (and yours) every time she eats and spits up! you could also take the bottle away every couple of gulps to slow her down, but you'd have to be careful not to do it mid-gulp so she isn't swallowing more air.
and if she already is using a slow flow nipple, you may want to look into getting a different bottle. some slow flow nipples seem to be slower than others. i found that evenflo, gerber, and parent's choice slow flow nipples came out a lot faster than the playtex nurser slow flow nipples. another thing to try (***but you'd need to check with her doctor first to rule out any other issues!***) would be to add a
little rice cereal to her bottle to thicken it up a bit. i did this with my older daughter but she was almost 2 months old by the time we tried that.
and for the spitting up and choking while laying flat, i really don't know what the statistics are. both of my girls were spitters from the day they were born, and i always worried about it. i had them sleeping in the play yard bassinet next to my bed and i do remember a couple of times when my little one would spit up and start choking on it. i rolled her to her side and she finished spitting up and was fine. we always tried to get her to sleep with side positioners, but she always wiggled back to her back. we ended up putting a folded towel under her bassinet mattress to keep her at an incline and i always kept her upright for at least half an hour after she ate, and that seemed to help her not spit up at night.
anyway, i hope it gets better for her! and congrats on your new little one!