In what state did you attempt to buy the shotgun? Federal law requires a firearms dealer to verify the identity of a purchaser. Your state may mandate a driver's license as proof of identity. It also apparently suspends the driver's licenses of those who owe back child support. Therefore, if you owe back child support, the state can suspend your driver's license. If you do not have a driver's license, the firearms dealer cannot verify your identity.
You might try again using a passport as proof of identity. You might also give everyone a break and pay the child support.