Oh, the above link and post above mine was cross posted (substantially edited 2 minutes before my reply, while I was writing).
So that answers the question.
I would
1. print the link so that you can show the gate agent that portable dialysis machines are allowed on board.
2. Consider not carrying much else on board. Even though you can legally assert that you can bring it aboard along with a carry-on suitcase and a briefcase/purse and an umbrella and reading material and food for the flight and a CPAP machine and a service animal, it is sometimes better to fly under the radar and slip your way into your seat. One way would be to carry the dialysis machine and a small personal item. That way, you can strap your briefcase or purse on your shoulder and carry the machine with two hands. It's up to you.