How to Get Baby to Sleep?

I have a daughter who will be 4 months old on november 1st. The past 3 weeks she refuses to nap and will not stay asleep at night. She used to sleep from 10pm until 5:30 am without waking now all of a sudden she is waking up every 40 minutes. In the day time she naps for about 10 minutes at a time. She has stopped falling asleep on her own and needs to be nursed to sleep. I took her to the doctor yesterday and he told me to try and introduce her to solids over the next two months because she probably needs more calories. She is 16 lbs 7 ozs and 26 1/2 inches long. Does anyone have any suggestions on how to get her to sleep? she seems to wake up with every little noise and she just screams. I dont want to let her cry it out but in desperation I have tried and she cried for almost an hour getting louder and louder and then it took for ever for me to calm her down. I don't know what to do anymore I am so tired all the time and I have a 5 year old who also needs my attention but I have to deal with a crying baby all the time. Her dad also cannot calm her down she cries even louder when i pass her to him. Oh and I also tried her on a little cereal last night and more got on the bib than what she ate. She also eats very frequently throughout the day. I think that is all the details I have so if anyone has any suggestions I am all ears.

Suggestion:

Eventhough she is only 4 months .. she could be teething and that could be what is unsettling her??

I use homeopathy and i would recommend trying it.. it is all natural
The remedy chamomilla is one of the main remedies for teething babies, it also helps when they are clingey and you cant put them down and.. it also helps to relax and sleep (like chamomile tea)
any age can take them.. so its also good for you to take to keep you calm aswell..
I dont know where you are located but I will post the link to a homeopathy website i use

http://homeopathyplus.com.au/pillules-b/ thats the page where you can buy the single remedies.. but have a look around ..

my bubba is 5.5 months and has slept so well overnight since he was prob 2.5 mths as we started a routine with him, where we bath him before bed say 6ish and used the bedtime bath by johnson and johnson's.. then kept everything quiet and didnt talk alot to him or play with him at this time so it didnt excite him again..he would have a feed then we would put him in the bassinette and have him wrapped up and have the room dark with a little nightlight on and just sit there and rock the bassinette till he fell asleep so he didnt get used to us nursing him to sleep.. light music might help too? ?
we did things like bath and quiet time at the same time everynight and now he has to be in bed by 7.30pm or he gets unsettled.. and he doesnt get up till 6.30 – 7 the next morning..

Hope some of that helps??? Good luck with it all