Hi and Welcome to Just Answer,
Ok, let's take a look at this;
It sounds like either your trap is clogged; you will need to remove it and clean out the obstruction. Make sure to have a bucket near by to catch the water from the sinks.
If the trap is clear, then you will need to get yourself a sewer auger from a rental place, or have a company come auger it for you.
As far as the wrench, it is made for when the garbage disposal is jammed.
Here is a movie, to install a disposal; at the end of the move it shows how to use the wrench.
Another thought would be to use a drain king. This will cause a seal in the pipe to allow the pressure to build up. These are only around 10 to 15 dollars. Best tool to have for the price...lol
If you need more help Let me know
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