When the pump runs but no liquid (water or antifreeze) comes out your pump is sucking air. Look for anyplace that there may be a loose connection. Check the filter that is installed on the line right before the water pump and make sure the top dome is screwed down tight. This is a frequent place for air to leak. If you did not blow your lines with air, just running the sink dry should not have made your pump lose prime - but if it has you need to get some water or antifreeze directly into the pump to prime it and get it pumping again.
If all else fails and you need to winterize right away and want to push fixing this off until the Spring, go to an RV shop and buy an RV antifreeze hand pump. One end connects to your city water line and the other end goes into an antifreeze bottle. You hand pump the pump and push antifreeze into your system. See this article - what you will read works for most RVs and Class Bs.
Winterizing
