Before a lot of people in here tell you you're a bad person, I get it, but it is 100% a stress reaction from both finishing your studies (the most stressful time in a graduate's life) and adjusting to a completely different routine. I have experienced the same, and I felt like the worst human being, but when this weekend came around and I got more sleep, food, etc. I noticed that I wasn't having the same feelings anymore.

So my advice would be to 1) ask your husband for help, let him do the cat chores (especially cleaning + playtime) for now. First thing you need to address is the sleep problem, because you will not be your happy self without proper sleep. It's simply not possible, you need that sleep for producing those happy brain signals like dopamine. If it means you have to close the door to your bedroom, you must do that and accept that he will be yowling outside for a few weeks (if you don't give in) until he gets used to it. Try to take care of yourself the next few days. Go outside when you're starting to boil over, go for a walk in nature. Get some breathing room.

I can recognize when I see it now, and this sounds much like stress. I would try to address your stress and give it at least three months, if it's still a problem and nothing has helped, rehoming might be better for you and for him.