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I suppose it depend on what purpose you are using the cotton balls for--that might help in finding an alternative :)

I used to use cotton balls for doing things like removing my nail polish...but I found that a regular wash cloth works fine for that, and is reusable.

Squares of flannelette?

I use a wash flannel for removing make-up-I have a handy little hook that it hangs on next to the sink.

Etsy has a handful of crocheted alternatives that are good for removing eye makeup.