Newborn wants to constantly eat

My baby is 3 days old and I only breast feed her and I notice whenever I put her down she cries and sucks on her fingers like she’s hungry after she unlatched herself after an hour of feeding. I try to put her down in her own bed but it’s impossible being that I’m always nursing her. Is this a problem? Am I spoiling her will she ever sleep on her own without being in my arms? How long does this phase last?