What can I do if I moved to another state and was told I was not able to have a restricted license?

I'm not 100% sure what your situation is from the brief summary you provided. But, in general, if Michigan has a hold on your license, that hold has to be lifted by Michigan before any other state will license you. If you have a valid restricted license from Michigan, other states can but do not have to honor it. You may be in a state that will not license anyone until they have full driving privileges from your former state, Michigan. If your restricted license expired in 2015, you should have reverted to a full license, unless you owe a reinstatement fee or have a driver responsibility fee suspension. To give you a complete, accurate answer, I would have to know the status of your Michigan driving privileges, and why your new state will not license you.