I might consider bringing more than 2 days worth of supplies unless you have a direct flight. You never know what could happen if your flight is late and you miss connections, or are diverted.

Bring your doctor's note describing the supplies, and go to the airport a little early in case security has a hard time understanding.

Medical supplies can be carried on. Again, it is possible the gate agent might need a bit of education.

Are you doing continuous cycling peritoneal dialysis, and if so, how big is your machine? You might want to contact the airline to try to get a bulkhead seat if in economy so you have more room and privacy and need to run the machine during the flight. I assume the machine has batteries; if not you may need to talk to the airline about power.

I'm sure your trip will go well.

Doc