We have an 8 week old pup, had her for almost 2 weeks now, and she screams and howls whenever I'm not next to her. I feel like I can't take much more of this, it's making our home miserable. We have not started working on a crate yet, she has a 3x3 exercise pen I use when I need to contain her, and I also have a baby gate between the kitchen (tile) and living room (carpet). She still pees anytime she gets excited, so I haven't been letting her into the living room that often. Anytime I cross over the gate she starts howling and whining. Sometimes she will settle down if she can't see me, but as long as she can see me there, she keeps going. It's turning into an ear-splitting scream. Same thing with the pen, if I set her in it, she just screams, especially if she can still see me. If she can't see me, eventually (10~15 min) she will settle down and nap. I have a toddler and sometimes I need to be able to separate them. I've read the crate-training article, should I just sit next to the gate until she is ok with it? How long do I let her whine for? What if she goes for 20-30 minutes without stopping? Thanks for any help or advice!
If she can see you and knows you are there, then this isn't separation anxiety - it is frustration-based noise about not being able to get to you. You really need to be working on separation like this regularly and daily and making it a priority in your training. You need to put the pup in the pen and sit right next to the pen, whilst working on a laptop or iPad and IGNORE ANY NOISE that happens. It doesn't matter how long it goes on for, pretend you are deaf to it. The pup needs to learn that this doesn't work. Have a read of this article I wrote and follow it, step by step - do not move onto the next step until you've mastered the previous one. And you can do this both with a crate and with her pen. https://thehappypuppysite.com/crate-training-a-puppy/
No, it can be very loud. The problem is that, if you respond to that level of loudness, the pup deduces that this must be the magic level of loudness which gets you to respond - so just skips to that level in future rightaway (as you've reinforced it!). I'd sit right outside the pen on the floor if you can, and just ignore noise.
Get some ear plugs from the hardware. Jo is right. If you don't ignore the noise, then you will end up training the dog to be noisy to get your attention. If she is traumatised, I would tend to the puppy. You'll know the difference.