Hi CJ,
It sounds like reflux to me, if you do a search you will come across a number of recent threads about it. Not being able to lie flat is definitely part of it, as well as agitation during feeding. Does she throw up ages after her feed? Are you holding her in a more upright position for either breast or bottle feeding?
Doc will probably recommend Infant Gaviscon, I am using this with some success with my 13 week ds. You can give it to a bf baby but it's easier to give in a bottle (either of expressed milk or formula).
To be honest, if I were you I would try and re-establish bf as it's very early days to mix feed successfully. Mind you, I couldn't get bf started at all so that colours my view on these things; I tend to think that my ds's digestive problems wouldn't be as bad if he was on breastmilk. However, you do have a lot more choices if you mix feed, in terms of being able to try different formulas and things. If you bf and it turns out she is lactose sensitive, I think you may end up having to cut lactose out of your diet so as not to be passing it on to her, I know this happened to some friends of friends of mine.
Have you been signed off by the midwife? If not, I would start with her, but definitely see the GP, it's worth giving Infant Gaviscon a try. (You can actually buy it over the counter, what I did was buy some when I already had an appointment to see the GP, so I could go and report on whether it was already working).
A sling can help to make life easier with a baby who prefers being upright; I must say I don't envy you with a 2 yo a well, our little one has nearly finished us off and there's two of us here full-time to share the burden.
Hope you get some help soon.