Whipped Cream out of Egg Whites
Carrageenan is a natural thickening agent. It helps the cream beat more easily and stay fluffy. I have seen brands that don't have it but I agree with Marti that you might have to try a health food store.

Egg whites do not beat to nearly the same consistency. They are much more foamy. If beaten all the way they are more stiff. If you are using the whipped cream on a pie you can make a meringue topping instead. It won't be the same but it will serve the same purpose.

Another alternative is to make whipped cream with evaporated milk:
The first link from Google

This technique produces cream that is similar to whipped cream- it has to stay chilled and be eaten right away. It will melt unless stabilized with gelatin.