I have decided that I'm not going to pay for half of the tow charges for my friend's car.
Why would you pay?
In the moment, I told her I would help her out, but on second thought, it wasn't my responsibility and now I don't think that I should.
It was kind to offer to help her. It's true, we're responsible for cleaning up our own messes in life, and shouldn't expect others to do that for us. However, because you said you would, it's going to hurt your friendship if you go back on your word.
That's cool, but I don't have time to deal with this bullshit.
You will have to make time to address payment for your friend's tow charges because you agreed to pay half. Reneging on your agreement is a breach of trust and that is not correct on your part. Pay your half.