Soak your hands in warm dishwater or go to Bed Bath and Beyond and buy a parafin bath. Usually used with manicures if you know a hairdresser, she might have one.
You put your hands in the warm parafin and it coats your hands with a wax. The wax will hold heat in. Will soothe the joint.
Or you can use a thumb plica splint when you are not quilting to allow it to totally rest. This looks like a carpal tunnel brace with a plastic insert that molds to your thumb. The splint holds your thumb.
Of course you can take something like Advil and use icy-hot or Biofreeze.
Finally try taking some hylaronic acid. Injuv is a popular brand name.
And you can certainly go the to chiropractor if it is jammed :-D If it is inflamed, I usually prescribe acupuncture versus adjusting.