need advice from other moms.

My 5 week old is sooo spoiled. I know what  people are going to say, "you can't spoil a baby!" Ok well that's your opinion. My 5 week old cries and cries and cries if she isn't being held. I mean honestly it's to the point where at night she refuses to sleep if she isn't in mine or my husbands chest. She won't sleep in her crib, her bassinet, she won't even sleep in our bed between us. She's HAS to be on one of us. During the day can't get anything done because she will cry and cry when I'm not holding her. She will be fed, have a clean nappie on, warm, she isn't gassy and the moment you pick her up she stops crying and is perfectly content. She won't sit in her swing or her bouncy seat, swaddling doesn't help her. If she falls asleep while we are holding her and we out her down in 5 minutes she's wide awake screaming and will refuse her pacifier. I'm going insane. She can not always be held and I do not want to end up having a toddler who refuses to sleep in her own bed and refuses to walk and demands to be carried everywhere. I know people say 5 weeks is to little to let them cry so you can teach them that they can not he bled all the time but I don't know what else to do. Plus anything I do will be counter productive because she's the first grandbaby. Anytimes she will see her grandparents (which is almost daily) they just hold her and hold her because they get to give her back and not deal with the consequences of her being held ALL THE TIME! I can't even wash my hair if my husband isn't home because she will scream the whole time not being held. What do I do?! How do I fix this? There are times where, this might make me a bad parent, but there are times where I just want to let her cry not because I don't love her because I do. She is my world but I can't just do nothing but hold her. Any advice is appreciated.