Pap Smears

Our office is a multi-specialty physician group and we do pap smears on Medicare, Medicaid, and commerical insurance patients. We are billing an office visit 99213 with a 25 modifier and then billing 88142. We are having issues with getting the 88142 paid. From my research it looks like we should not be billing the 88142 and should be using G0123 for Medicare. Should the 88142 be billed by the outside lab company reading the pap? Is this correct? What about Medicaid and commercial insurances?