Cockatiel with diarrhea.

honey... I don't even own a cockatiel yet, but I already see big mistakes. For one, the cage is too small. I recommend a cage that size for 2 finches, maybe not even that. Also, here is your BIGGEST mistake, if you didn't do this : quarantining your birds. At the shop, a cockatiel might have a disease or sickness the owners have not yet told you about, and that is why when you plan on getting a 2nd bird, you must quarantine them. This explains how your other cockatiel got diarrhea, too. Also, the water bottle. Water bottles can collect bacteria from the air and moisture collecting inside of it, and that may be a problem that both are experiencing. I am afraid that your only option here is to take them to the vet. If you don't, but not to guilt you, they could die an agonizing death.
Best wishes from me.

And while we are talking about cages, you absolutely NEED to get them some toys and a bigger cage! If you cannot afford to keep a cockatiel, you should NOT get one, and you got TWO! I got a cage and about 8 toys off of Amazon for around 150 to 200 dollars, and the cage was 80. If you are feeding them seeds and pellets, or just seeds, they might have fatty liver disease, and that requires a vet visit. I think they could have fatty liver disease due to their alarming size. They could just be puffed up, but that still could pose as a risk. These birds do NOT look happy, and I hate to tell you this.

Please oh PLEASE, if you are going to keep them, get them new perches and toys, and a new cage. This looks like an impulse buy and if you cannot upkeep these birds, REHOME THEM!

Forgot to mention... if you're giving them eggshells without treating them, they could have salmonella from the whites and maybe the yolk.