Most definantely carry on your breathing machine and your meds. You do not want to be delayed or your luggage lost or delayed and you needing your machine. Meds can too easily get lifted from your suitcase. Unfortunantely the screeners themselves sometimes aren't screened to well.
My girls have flown by themselves a few times in the last couple of years. Meds should be in the original container. If you get giant containers, ask your pharmacy for a small empty bottle with labels so you can just transfer what you need for your trip plus a few extra days. Always take a little extra along. Depending on how long the trip is, I have mailed meds ahead so Rachel didn't have to carry much. Like spring break and she was going to be staying with family in FL. If it's just been a couple of days, we have skipped the percussor and just used the flutter or acapella.
Depending on the airport, some security checkpoints want you to remove your machine just like your laptop, others don't. I look for the sign and if there isn't one, I don't remove it.
We travel quite a bit and I have only gotten a meds list from the doc for international travel and if we are needing to carry IV meds. In one case no one asked to see it for the IV meds but on the return flight from a diff. airport they did. By the way, Rachel flew that by herself there and with her sister on the way back.
Someone else mentioned water. Always try and buy a drink before boarding, most supply a drink but it can be a good half hour into the flight sometimes. Take along a snack or two as well because most don't even serve peanuts anymore.
I use the travel anti-bacterial wipes or clorox wipes and wipe down the tray,seat pocket, buckles and arms once I get in the seat. Good thing to do for anyone but to be honest I only started that when Anna got her transplant and after seeing how dirty it was, Eeewww, why didn't I do it before?!
Once you get the hang of it, it's really a breeze. Rachel will fly with a carry-on bag with everything inside and her laptop. No checked baggage. But her machine is really small. She has a travel size one and it fits in a small bag about the size of two little camera bags. I think it doesn't even weigh a pound. And she crams her purse into her laptop bag. So since you are checking your luggage, you can possibly get away with a backpack.
Have a great trip!