Newborn constipated or upset tummy?

My newborn daughter is 12 days old and she has been extremely gassy the last few hours. Shes had these really deep loud farts but she hasnt pooped at all... She has ate a lot in the last few hours as well and has pooped at least 4 times today. Is this a sign shes becoming constipated or is her tummy just upset from how much she has ate and either way, how can I help to soothe her so we both can get some sleep?