I think what you're describing is perfectly normal.
You can't stop age appropriate behaviours, and they're both going to want your attention, and you know that.
The thing is your children don't need you at your best, they need you at your most regulated.
You being regulated means better coregulation for them when they are fighting, bickering, climbing the walls and being willful little boundary pushers.
You might benefit from things like loop earplugs, or ear defenders. They don't totally block noise out, but when kids are loud or argumentative, it just takes some of that buzz away, and it also gives a visual cue to the kids that they need to be quiet. This is one I use at home. I put my ear defenders on, I cross my arms and give my sternest Paddington bear stare, and I don't talk or take any action until it has calmed down.
If it extends to physical or harmful behaviour, I pick up that child and I take them to a corner and I say if you hurt me/them/us, then you can't be near us. Rinse and repeat. Ear defenders still on because I'm not about to get overwhelmed with any tears or screaming. It's just a consequence of the actions.
My mum used less conventional methods, but they still worked. She used the talking stick. Whoever held it could talk. When chaos descended we got stuck on the sofa with a plastic envelope that had paper and crayons, seated at opposite ends, while she took herself off into the kitchen for 5 minutes.
Ultimately, you don't have to copy any of my suggestions, the important thing is finding something that works for you, that doesn't resort to shouting, it isn't targeted at either of your children, and it just breaks that cycle instantly so you can get a moment to get your head straight.