How can I get my quad to stop swelling?

Find the Cause. A muscle that swells does so for a reason, which will determine the best treatment. Common causes are injury, overuse, infection, inflammatory problems and more. You will need to see a orthopedist to make the diagnosis before the best treatment can be determined. Often icing, gentle stretching, nsaids and a wrap are helpful. Being seen by and orthopedist is key to success !
It depends. Start with being examined by a sports medicine trained physician, who can determine the origin of the swelling. If it turns out to be musculo-skeletal in nature, then icing, an anti-inflammatory medication and physical therapy should take care of it.