Anyone struggling with a pet and a newborn? 😞

FTM here and I have a 4 week old baby and adult cat. I've been struggling with the adjustment of being a mom and caring for a newborn and lately my cat has been a struggle I'm starting to lose control over. He's become extra needy and I give him all the attention I can by playing with him and grooming him but as you can imagine, I dont have all the time in the world to dedicate just to him. I'm also going nuts over the fact that his fur is EVERYWHERE and I'm going insane over the cleanliness of my baby's items. There's fur on baby blankets and almost everything my son comes in contact with and it grosses me out. Also, my cat has become defiant and is doing things he KNOWS he shouldn't. I woke up at 3am to grab a baby bottle from the kitchen and I found my cat on the counter, wagging his dirty furry tail all over my clean bottle parts I left to air dry. I'm going absolutely insane trying to discipline this cat while taking care of a newborn while also trying to be EXTRA clean when it comes to washing/sanitizing. I got so fed up with my cat that one night I put him in the bathroom with all his necessities and locked the door bc I caught him clawing at the bassinet, waking my son up after I spent over an hour rocking him to sleep. I feel so guilty about the feelings of resentment towards a cat but I'm so stressed beyond words.

Sorry for the vent but I really needed to get this out 😞