Yes the older child could get it if he has used the bottle.
Not only that but anyone with a weakened immune system(even a COLD) can get it. It will attack the skin and is NOT easy to get rid of.
I know this from experience.
One of my daycare kids had a yeast infection. I got a cold from another daycare kid and then got the yeast infection from helping to treat the kid with it. I ended up COVERED in it and the itch was intense.
I couldnt sleep, I couldnt eat. It was on my scalp, legs, arms, everywhere. Getting through my days was miserable. I finally drove myself to the ER, after being told by my own PCP to try OTC remedies for athletes foot which did not work for poop!
They took me right in. My BP was ski high. I hadnt slept in two weeks.
They gave me sleeping pills and two tubes of nystatin. PLUS a Rx for more. It took 3 days for me to get it all. And once ya get it THAT badly, from what I have read and been told. And noticed. It never really goes away. I now have a ongoing Rx for the nystatin. I keep tea tree oil in the house at ALL times(helps with small outbreaks) And diet plays a big part in managing it. Diabetics tend to be really susceptible to it. Another reason I still test my blood sugar levels YEARS after having Gestational diabetes. I am now paranoid about getting another outbreak. I would rather be in pain than deal with itch that intense ever again. Hell mosquitoe bites drive me nuts. Poison ivy? summack? Yeast is worse. I would rather cut myself with razors than deal with itch like that again