Only if Sheila's arm was across her chest ( in a sitting position ) head bent, which would have restricted the blood flow from her injuries. It may have come from her mouth,as it would drip out if her head had been bent over.
If you sit up,put your arm across your chest,head bent forward,and if your mouth contained blood it would eke out,particularly if Sheila was gasping and not able to expel it in the normal way.
When she'd been placed in the lying down position the overflow from the restricted neck position would have then pooled as her head and neck rested on the floor,as she hadn't been dead long enough for the wound to have been plugged or halted by LM.