Yeah, it's somewhere along the median nerve as your symptoms are within its sensory distribution. As was said, it can commonly come from the carpal tunnel, or it can come from the elbow or even the neck or a combination. The carpal tunnel is packed with the median nerve and a whole bunch of flexor tendons for the hand. When you're filing for a long period of time, your finger flexor tendons stay flexed as they try to hold tight to the needle files and take up more space in the tunnel. There's not a lot of space to begin with, so after a while, the nerve starts going to sleep as its blood supply is decreased. Bigger handles on the files will help, for sure.
Also, be aware of your posture as you typically might be bent over and flexed at the neck for a long period of time while filing. Try to find a position that is neutral. If you are putting pressure on the nerve up higher (say, in the neck), you will be more likely to see symptoms distally (like the carpal tunnel). That's called a double crush in the business (I'm a Physical Therapist, by the way).
If it is truly carpal tunnel issues, avoid full finger flexion for a while and do some finger tip hanging stretches (use just the finger tips to grap onto the edge of the molding on the top of a door frame and gently hang on your finger tips with the rest of your fingers and wrists straight. Also, median nerve flosses will help. I'll see if I can find some pictures of one as explaining it can sometimes be a hassle.
--nathan