My cockatiel Pepper does breath hard after flying around room, but vet did tell me he was a little over weight around chest area and likely the reason, but he is bigger then the others. Thankfully it did take a while of flying and out of cage time but he did dropped to normal weight right under a 100 grams. They clipped him when I received him, so he needed the exercise to get back in shape pretty much.
Yes flying will cause heavy breathing and watery poo as they don't drink water till back in cage, or on tree stand and then take a few drinks. Then poo back to normal. Watery poo maybe normal if they are slightly dehydrated from strenuous activities, such as flying. My U2's usually even Droop wings when exhausted, or overheating which they fly back to bench then I mist them as here can get up to the 90's outside in the summer, or I bring them inside to cool down for a while and give them some water to drink.
If it all the time she breathing hard and can hear it, get her to a vet. My Cooper umbrella cockatoo had issue with breathing and sneeze and wheeze turn out to be a upper respiratory tract infection and he also had a yeast infection as well when they did a few tests. Thankfully noticed it on the first day of getting him as notice he was breathing much louder then my other U2 one nare was pretty much closed. So ran him over to the vet and after treating him, he was better after about 3 days showed improvement and a week breathing normally and nare now wide open.