Yes, it's probably surprising to hear about a parrotlet being excessively loud. I am new to owning birds but I did do a fair bit of research on parrots and parrotlets before acquiring Carl. The first few days were alright, he chirped and trilled, but never very loud. I've no issue with noise, but the volume is a concern.
The last few days or so he started shrieking at the top of his lungs. A lot of parrotlet owners will probably say that parrotlets don't shriek, but mine will chirp at the very top of his lungs over and over and it's so loud that I can hear him outside my house from the street. I assume this is his contact call, but he does it even when I am in the room.
This call is so loud that when you're in the same room as him it's actually physically painful
Parrotlets are considered good apartment birds by a lot of people but from my experience I may as well have gotten a macaw
I have been ignoring him entirely while he makes noise and praising him with millet when he is silent (we are still new to each other so verbal praise isn't as effective yet) but his behaviour has not changed. As for interaction, I clicker/target train him 3-4 times for 15-20 minutes daily and spend a good chunk of the day in the room often talking to him. He will often just start shrieking mid-conversation, forcing me to leave the room until he's quiet again (which can take up to a half hour).
I'm at my wit's end. If I can't train him out of this in the next 2 weeks (I move into an apartment at the end of this timeline) I will be forced to rehome him by my landlord.
It's not the fact that he makes noise, because most of his sounds are cute and not very loud, but when he shrieks it's just unbearable. They're not kidding when they say there's a full sized parrot living in these guys.