I am not a teacher.
For the examples you have given, yes. When you are actually lacking enough of an item, you can use short of or short on. I grew up hearing "short on" in the United States, while "short of" may be popular in other areas.
There are other uses of "short of" which definitely are NOT interchangeable, here are a couple. You would not use short on for these idioms.
"A sandwich short of a picnic"
"He fell short of the goal"
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