I agree (again

) go back to your doctor and insist on having her checked out. I don't know but I thought you had to pay for medical help in the states, not like the NHS we get. If so I would be even more adamant that they do as I ask, as your paying the bill!
I did think she could get to sleep on her own, I knew you rocked to extend her sleep but thought she was going to sleep initially independantly (albeit with you in the room) So if you are rocking her to sleep for every sleep then yes, this will most definitly be a lot of the reason she is not sleeping well or long enough. You do need to get tough and at her age it isn't going to be pretty but it can be done. I would post elsewhere to get a better response but just to get you going, this in a nutshell is what I would do. The fortunate thing is she is sleeping so badly and is already so OT then it really wont matter how long it takes her to get to sleep because it can't get any worse than it is.
Basic plan - Sorry if I'm teaching granny to suck eggs here but here it is anyway.
Start with your wind down, if you don't have a good one then think one up and stick with it. It doesn't have to be complicated. Lily's is; in my room, read 2 books, into sleep sac, she used to then be bf but when I stopped that we started having a little chat about what we had done so far that day. Then into her room, turn on night light, say good night to almost everything in room

then I sing Winnie pooh theme song we have a cuddle then I lay her down say night night and leave. So after your wind down lay her down and step back. If she jumps up happy turn your back and head for door. She will then most likely cry for you to come back, lay her down and repeat. If when you lay her down she is still crying and jumps straight up lay her straight back down and rub her back or stroke her head, whatever calms her. As she starts to calm down reduce the pressure of rub or stroke and see if you can stop before she falls completly to sleep, if not for now rub her to sleep. Wait a good 10mins before leaving the room. If she then wakes after 30mins happy then leave her to it until she cry's for you, then go in and lay her down and repeat the whole process until either she is asleep or you have been at it for at least 30mins. When you decide to get her up if she wont go back to sleep try to do it when she is not crying so that she doesn't think crying gets me up.
For NW's I would do exactly the same, exept that when It was in early hours I would stay in her room with her lay down on floor and pretend you are asleep if she is just up and happy but not sleeping, lay her down if she cry's and rub etc to help her settle, do this with ear plugs in it really helps. Whats hugely important at her age is to not give in, you have to be totally 100% consistant, every time you give in just for some peace and quiet and to all get some sleep you will go 10 steps back not just 1!
Once she can settle to sleep in her cot and not by being rocked then you can start with the GW, don't leave this too long as your presence in her room will soon become more distracting to her than helpful. So start by only rubbing or stroking for a few minutes after initial lay down, then stand up beside cot and make no eye contact and do not talk to her. The hardest part of GW is breaking the 'contact to sleep' part once this is done it should be a lot easier to get out of room. Then with every sleep time step just a little further from cot until you eventually lay her down and walk to door but still don't leave until she is asleep. The next hardest part is getting out of room. Once she is happy that she falls asleep with you at door you then take the plunge and step out of the door after laying her down. You will most likely have to go back in and may need to repeat several steps but this time keep heading out of door after laying her down. It then becomes WI/PD/WO. So what I found was that I would wi do pd and walk straight back out crying or not, then straight back in and repeat until she gave in and fell asleep. Obviously if she gets too upset at this point to be able to settle herself then you will need to calm her before leaving but be wary of this because they quickly figure out how to keep you right beside the cot by keeping on crying.
Once you are at the wi/pd/wo stage do this for all wakings, from naps and nws and ew's. Even if Lily wasn't crying but woke up at wrong time like halfway through a nap or ew (always crys for NW) I would still wi/pd/wo as a reminder that its not time to get up its still sleep time.
If you are super consistant with is it shouldn't take too long before you start to see results but like I said if you give in just 1 time you will seriously pay for it and have to go back and repeat earlier steps until you catch back up.
got to go Lily crying, let me know if you need any more advise on GW
