How To Get A Noise Barrier In my Community
Yes, contact everyone you mentioned and ask them who else you should contact. These projects are prioritized, budgeted and then approved. In order to get to the top of the priority list, you need to find out who makes the list and who determines what is important. 

First, find out if it's a state or federal road. They are your target. Contact them and ask for help. They can guide you. 

Then, I'd hire a TRAFFIC Engineer to get his advise. He can have a sound test completed. If it's a noise issue, I'd contact your town, or surrounding towns, to see what the ordinances are for noise. Yep, every town has a noise disturbance law. Then see how it compares to your local noise disturbance laws. 

Your Traffic Engineer can prepare a cost estimate, which will enable you to get started with the appropriate budget committees. 

Also, contact your local government representatives and ask for their help. 

This is a long process. I'd guess it will take 2-3 years before you see progress.