S.,
I have four kids. 11, 10, 6 and 4. My insurance paid for them to get tested. My six year old, at the time of the test, came back positive. It was because we lived in an older home. Since we moved, the levels went back down. The doctor said it does not matter where you live, you can still get lead poisioning from any where.
I would push the fact. Since you work, that should be cause enough to get tested. Even if the insurance does not pay for it, ask the doctor how much it would cost to get it done. Maybe you can make a payment arrangement with them.
Not knowing, and if you have to take your child to the emergency room for any reason, and they find lead poisioning in his blood, it will come back on you. Take the test, and this way you are also covered. You won't have to worry about it anymore.