Definitely sounds like a warble to me. Yuck. They are often seen in mice, rabbits and deer but can get into cats and dogs. They enter via the mouth or nose or into an open wound and then grow. They stick their heads out to get air every now and then. They eventually leave their host at some point. I looked it up recently because my cat caught a mouse outside and killed it and two of these creepy things crawled out of the mouse's side and they too were about 3/4 of an inch in size. The mouse was so small, these things made up a 1/4 of it's body.
I hope they keep the wound clean now that the worm is out.