let it dry out as much as possible and put it in a south facing window if not already there. You can trim off the side branch but I would leave the top one. My Hass is doing something similar. The least amount of water will prevent tip die back. Which leads to the branches dying back. Hopefully yours will hang on until spring!

Sorry to tell you, but your tree is definitely dead - or at least in the process of dying. I see you have a bag of fertilizer there. Did you recently fertilize it? Avocados are very sensitive to salt build up and will experience salt burn when you fertilize them. Too much of it will cause necrosis to travel from the roots, up the stem and out toward the tips of the branches. From the looks of it, your tree is experiencing this as the trunk is dead and the extent of dead tissue is progressing toward the branch tips. This is even an issue here where we grow avocados in the ground. A friend of mine sprinkled fertilizer on the surface of the soil near his 10-foot avocado last summer. With all the rain we've had, the fertilizer dissolved and soaked into the ground, causing the avocado to burn and die - a whole 6 months later. It is best to not fertilize young avocado trees at all.