What to should you do if you chip a filling?

I was recently doing my everyday work of repairing xbox 360s and I was going to bite down onto a small strip of electrical tape to tear ir and noticed something in my mouth. At first I figured it was a piece of the tape by my gums and as I went to fish it out with my tongue it pushed the chip back down. After a few seconds with a toothpick a small thin layer of my tooth fell out of my mouth. I think its the a part of the filling that was in my tooth, but Im not certain.

I have a lot of plans today and I dont want to have to have my teeth drilled again as I have serious anxiety and it drives me crazy. If i go to get it repaired will they have to drill again or can they refill it? What will happen if I wait a few days?

It doesnt hurt it just feels a little rough where the chip came from.

Any advice at all would be greatly appreciated, thanks!!

thanks!