It's a very safe bet that you you have a thru hull transducer- meaning there is a hole in your hull and the transducer is in the water. Unless it look like this.
https://www.starmarinedepot.com/low...mngVZX43ydxswEBNKFcq9WrU6ds3SnqRoCdoUQAvD_BwE
While the shoot thru, or 'in hull', or whatever you call it also need to be leveled, I can't imagine it ever being done with wood fairing. Because you need the cup of oil between the xducer and the hull.
You didn't by any chance paint over the "something sticking down out of the hull", did you? They make a special bottom paint for the transducer. If you painted over it with regular bottom paint, that may be your problem ( probably not though, they should work thru a coat or two of paint)
What do you mean when you say it's not working ? It is not giving an accurate reading, not giving any reading, not powering up? As far as I know, there really aren't any moving parts, or other parts, in a thru hull depth transducer to fail ( except the speed sensing wheels) - so as long as you didn't paint over it, or break it by smashing it on the ground - not sure how you can be sure the problem is the transducer and not the wiring, or the depth finder itself?
I would not try to change this one in the water. If you put it in yourself, and know what sealant was used, perhaps. I once tried to remove one on land ( because it was 35 years old and the unit it was attached to was being replaced - the xducer still was fine). The previous owner had used a 5 gallon drum of 5200 it seemed. There was NO way this one was coming off without taking a few feet of fiberglass with it. I just let it be, and put the new one somewhere else. Transom mounts work very well on some boats, 100x better than the shoot thru, in my opinion. Just be sure you mount it correctly. Yes, it takes a LOT longer to do it right - but if you don't you will most likely destroy your transom. Correctly doesn't mean a little sealant on the screws. Thru bolt, seal the core, the whole enchilada.