Does the wire you installed cross any electrical power lines? If so, that may be the cause. Another and more probable cause is that your Television is not grounded. Since the radio in your Airstream is DC, it is attached to the same grounding plane as the rest of your trailer, and just like an automobile, all the components need to touch the same plane. I am guessing the Television is AC. If that is the case, a filter such as the ones sold at auto parts stores attached to the input line from the Television to the radio may solve the problem.
Craig and Carol
1997 34' Excella 1000
1970 27' Overlander, International
2009 Ford F150 5.4L
ProPride hitch with 1400# bars
Past President Southeastern Camping Unit (12)