I am so sorry this happened to you! I did the same thing a couple of years ago and went into a panic! My DS who was 12 at the time, kicked me out of my sewing room, eased the fabric out, got the pin out too. It was stuck in and under the dogs. Kept that pin as a reminder not to do that again! Ironically, that exact pin paid him back! Nasty knot in something of his a few months later and it was the only thing to give me the leverage I needed.
Hope you are back to sewing with your favorite machine soon!!