baby's head flat

My sons head is flat and we are currently in the process of TRYING to get a helmet although the insurance denied it. Anyways, he doesn't sit up on his own yet (he'll be 6 months on April 27th) and was just wondering if anybody else has ever been in my shoes and did their baby's head round out on it's own as they got older and was able to sit up and stuff more?????? 
I feel even guilty him being in his swing, laying down on his back, being in his car seat!! It's horrible and we do tummy time but not for long because he's able to roll right over.