Yeah, I knowUsing boiling water on silk goes against everything I ever learned about silk. The scarf I used for practice was very thin silk, and I didn't get a hole in it, NOR did the texture of the fabric change.
How old is your scarf, what design is it? What colors?
I have NOT used boiling water on any of the following scarves, but HAVE washed them.
Grand Apparat from the 1970s, (I think) white background with black and gold and soft yellow and some gray
Voitures a transformation from the ???? (pretty old scarf, 1960s I suspect) white background, black, beiges
Poste et Cavalarie from 1980s, white background with black, gold red, wine -- this one was a TOTAL mess when I got it, black smears and crud and smell, and old makeup stains (including lipstick, I suspect) and it came out great, with no bleeding
Romantique, quite old, white background with blue, yellow, pink Dies et Hores/Astrologie -- newish issue, black with some white and gold
I use cold water and (I can't believe I'm going to admit this in public) CLEAR dish soap. A gentle dish soap, like the Clear Dove or Clear Ivory.
Ultimately the decision is going to be yours, to wash or to dry clean. For me, I don't have a huge investment in any of my scarves (estate sales, thrift shops, ebay) and none of them has sentimental value. So .... for me washing is the better choice. Only you can decide about your scarf.
My very very dirty one with red dye run is LA PROMENADE DE LONGCHAMPS. Judging by the level of dirt it is prob from 1965!
I do hear the dish soap is good for getting the oily stuff off fabric. So I think you did good! I am just too afraid to see MORE red transfer after the wash.