Flat head birth defect

ok Moms help me out here! My daughter is 4.5 months old and her head is a bit flat. I'm trying so hard to fix her head positioning every night, waking countless times to see if her face is turned. Please please tell me her head shape will get better from here even if it's a bit flat. Her doc recommended us to a specialist but we don't think it's necessary to take her because we don't think she'll need a helmet and it could be costly. we are working hard at turning her head when she sleeps. I switch her position on the crib every week. I got a notification from the hospital saying my daughter has a birth defect------> flat head. Since when having a flat head is a birth defect??? Apparently her doc had initiated this and I received the notification to take her for therapy and services. I'm thinking of changing her doc.