What's the best way to deal with my new, very loud neighbors?

A few weeks ago a couple moved in the apartment above me. Ever since, my boyfriend and I have not been able to get a full night of rest.

The very first night, they accidentally set their radio alarm clock for 3:00 am and weren’t home to shut it off. It was very loud. We had to leave our bedroom and go attempt to sleep in the living room with our tv on. Even that didn’t cover up the radio. We left a note asking to please be curteous and not set an alarm that they wouldn’t be home to shut off. They later apologized.

The very same night, we were startled awake by very loud thumping and screaming. Our apartment was shaking from the pounding. They were having an argument. At 5:00 am. It lasted 2 hours. At least a few times a day the same thing happens. During the day, it doesn’t bother me as much. But when I’m in a dead sleep and get woken up by my walls shaking and people screaming, I’m irritated to say the least. I’ve been going to work completely exhausted.

What is our best option? Do we tell the landlord the situation and hope she takes care of it? Or is there something else we should do before possibly getting them in trouble/evicted. All I can think about is once my baby is born, I’ll be thankful for any sleep I can get, but I’m sure it’ll be interrupted by the neighbors. I cant go on like this forever and it doesnt seem to be dying down. Any suggestions?