Ticks should be removed entirely becaue any part that's left inside may cause infection. I suggest that you take Tommy to the vet where they can take out the rest of the tick (if it is still there).
If you happen to find another tick sometime, here's a tip that my vet has given to me - get a cotton ball moistured in cooking oil or kerosene (which is better) and cover the tick with it. After about 10 minutes the tick will die and will soon fall out by itself. You can also tweezer it out by carefully twisting it in one direction.
Good luck and my fingers are crossed for Tommy!
Tina - flashy fawn, natural ears, born October 1996; the sweetest thing!