Not A Happy Baby

My Daughter is 4weeks old on Friday, and I've had many sleepless nights. (Welcome to motherhood). She had a great day yesterday wide eyed and happy most the day when she wasn't sleeping. Me & My Fiancee got some decent sleep the night before last too as she slept 3hours each time from 4pm on 16th through to last night 12, but once I'd popped her into her moses basket last night she woke up at 2am as usual i changed her feed her as usual and she drifted of but once I poped her into her moses basket she was crying and and off all the way through to now where its still carrying on.
Shes had what 2 hours this morning but 1 hour at a time. Last night she was crying anytime i was putting her down. if her dummy fell out shed cry, i nearly fell asleep with her in the bed cause she seems to calm down sometimes when in my arms laying in between me and my fiancee, which i know i shouldn't do but I don't have the energy to sit up and stay awake with her.
My Fiancee has tried taking her but shes the same with him.
I have tried feeding her, changing nappy and a bit of a cuddle. but still she screams
but still the crying was going on.
I've tried ingoring her but after 5 mniutes i cant take it any longer and pick her up, i've checked her tempreture its 36.5c which is around normal i think. she's been teething quiet a bit too.
Not A Happy Baby Today :(
Sam's Making Pie&MAsh So at least I have something to look forward too Yummy!