I found this: I'm no good at identifying anything but wool, myself;

Silk
Is a protein fiber which burns slowly and curls away from the flame. It leaves a dark bead which can be easily crushed. It is self-extinguishing and leaves ash that is a dark, gritty, fine powder. It smells like burned hair or charred meat. It gives out little or no smoke and the fume has no hazard.

Also, silk has an odor when it is wet. To me, it smells just like what you might it expect it to smell like, given where it comes from. Animal fibers do tend to give off an oder when wet, think wet wool. Wet it down and take a whiff to see what it smells like.

By all means, give it a wash. Silk actually washes up quite well! And, of course the burn test is another good thing to try.

I thought that wamsutta made things like sheets and towels and such. I don't think that I have ever seen it on the selvage of a garment fabric, but if it feels good and will work for a garment, give it a try.

But, if it is more of a furnishings fabric you might not find it very comfortable to wear. Nothing to lose by giving it a toss through the wash and the dry and see what happens.

What is it about the fabric that makes you think that it might be silk?

If you want to wash it, I would cut a small sample and wash that first. Most silk will never be the same after washing, but this might not bother you. However, once it is washed, subsequent washings will not change it as much as the first washing.

Silk is hydrophobic, meaning that it does not like water, unlike cotton or linen, which are hydrophilic and are therefore more easily cleaned by washing in water.