What is the term for taking it out on someone even though you will be harmed by this too?

"Cutting off your nose to spite your face" comes close to what you are describing.

For a single word, you can consider spite, which means to go out of one's way to harm another for a perceived wrong.

In other words, it means to do something unnecessary (which means there is a cost) to harm another for what may be no legitimate reason at all.

An example is the spite fence. This is a fence that is put up for no other reason than to annoy a neighbor. It is generally done so at some cost to the one putting it up (for the material or at least the for labor).