Separation Anxiety! Help!!

LO is 3 years old and she can’t be at home in a room just for 1 minute by herself. She demands a lot needy attention. She’ll start to cry otherwise. Running to the bathroom or going downstairs for a snack it’s impossible. At first we thought it was a phase but it hasn’t improved. We have 2 other infants to attend to and it’s driving us off the wall! We have told her this is our home and sometimes we have to go to other room do something and it’s ok for her to stay where she is and continue playing. Sometimes with distractions it works and other times she drops everything to Tag along. Is this normal? What to do?