When you say oil do you also mean waxes? And is there a difference between plant and animal oils? What about wax like in candles?

The difference between oil and wax is whether they are solid or liquid at room temperature. Higher saturation fats are more likely to be solid at room temperature, and longer chain fats are the same, so a long highly saturated fat is likely to be very solid at room temperature and therefore hard and waxy.

I find that vegetable oils excluding olive oil are pretty awful on my skin, but animal fats tend to be less of an issue. Tallow and coconut oil are my favourites for texture for animal and plant respectively, and while butter is OK ghee is strangely nasty.

even if a tiny droplet touches my hands my day is half-ruined