Right .... just so this never happens again.
Always hold the finger you are working on with only these 3 digits. The thumb, index and middle finger.
Place the thumb and index finger each side of the finger you are working on, and the MIDDLE finger .... put it under the finger you are holding and lay it on the underside for great support PLUS it never gets in the way of the abrasive so it never gets filed!!
Also, the elbow of the holding hand should not be at your side when you are working as it gets you all bunched up and you get in your own way. Whilst holding the finger in the above way, make sure your elbow is resting on the desk and in line with the desk. This opens up a huge window for you to work in and you should never get in the way again. It really works and is a whole lot more comfortable for you and stable for your client. HTH