Agh.. this will be a little crazy about my life right now...
A therapist is a decent idea. In fact, that is a form of grounding. If you are the type of person who feels better after sharing something painful, then I would say you will benefit from a therapist.
It sounds like you have two hectic phases doing the most damage in your life right now. I’ll ignore school as it is what it is. And I’m sure you know that after you tough that out you will be able to get a better job and move out of your parent’s home (curing those two situations). But in the meantime, your home life is negative and stressful. As a college student you probably don't have a choice financially right now so you'll have to stay there until you make enough money to leave. But you can survive by being busy and staying away from your home as much as possible (thereby limiting your exposure to that negative).
As for your job, sometimes the crap hits the fan. The stars align, the perfect storm hits, and you are dealing with multiple problems at the same time. You could change jobs and do something easier and quieter (like work in a library or book store). But consider this, we all are given challenges to overcome in our life paths. Some people run away from every sign of trouble and never learn how to work through challenge and conflict. By working through these work problems one at a time, you are returning everything to normal. You are an agent of change and are working through the challenge and gaining momentum on your life path. You may just learn a valuable lesson or two there that will level you up so to speak so that you can rise to a more important challenge or job down the road. And it is no coincidence that you as an empath are thrown into a situation where multiple people are upset. Your gift is to change that energy, calm everyone down, and return the workplace to peace.
Now, it is definitely hard being an empath. You absorbed all the crap from your family that morning and then got hit with all sorts of negative at work. And the more you take in the more anxiety you get hit with. And that was all on top of the anxiety you carry from being a busy student trying to do well in school. My advice, make sure you fit in grounding meditation and physical exercise each day. You have to get rid of that negative that you take in so that you don't get overloaded. And as for your family, try your best to limit time with them since they are so toxic. Try to have dinner out with friends instead of with them once in a while and study in a library instead of at your home. You will notice a big difference limiting your time in that pressure cooker. And then one day you will be able to move out and remove yourself from that environment.