If the thingy sticking out of the ground is about 6" diameter then you have a deep well with a submersible pump. If there was a lot of sinking in the ground then it could have damaged the pipe that runs underground from the well to the house. If that is the case it won't fix itself. It this is what you have then that is the well casing sticking out of the ground and the well is way down below the water level.
If the thingy sticking out of the ground is 2 or 3 ft in diameter then you probably have a shallow well and the load could have damaged the the well or the pipe. If this is the case then you should have a pump in your house or basement.
Someone needs to look into the top of that thing to see if any damage is apparent. They next thing is to dig down below the frost line in the area adjacent to the thingy sticking out of the ground to see what needs repair.
I don't know what your arrangement was with the tree man but he should have known not to run so close to the well. He might feel some responsiblity to fix it.
Come back and tell us what you fine about the kind of pump and well and you may get some more suggestions.