Beeswax by itself generally does not produce a stable emulsion.
If you can't tolerate reliable emulsifiers like ewax/polawax/BTMS (have you tried these? How do you know you can't tolerate them?), then you might consider a solid lotion bar of beeswax and oils or a salve with the same ingredients.
You could also try a whipped butter without any water - say 70-80% shea and the remainder a liquid oil.
We also need to know a lot more about your method to trouble shoot. Did you heat and hold your ingredients? Did you use a stick blender or some other method for mixing? Also ingredients should be by weight, not volume and even better if you can convert them to % form.
Just eyeballing it, your ratio of oil to water seems a bit high. I can't comment on the amount of beeswax because I don't use it in lotions.
If you're making a water based product you also really need to use a preservative. Even if you use it up in a week. Even if you keep it in the refrigerator. Just because it looks fine, doesn't mean it is fine. The most effective broad spectrum ones involve parabens which you said you can't/won't use. You might consider liquid germall + which does not include parabens. There are also some other more "natural" preservatives available to the home crafter that you might want to investigate.
A solid lotion bar or water-free salve would not require use of a preservative.
Good luck with your next formulation.
Edited to add this link. This blog has great information. Check it out!
http://swiftcraftymonkey.blogspot.com/2 ... otion.html