The list of ingredients in Tertius are: Stearic Acid, Beef Tallow, Goats Milk, Shea Butter, Potassium Hydroxide, Kokum Butter, Mango Butter, Glycerin, Cocoa Butter, Castor Oil, Manteca (Pig Fat), Strangisto Giaourti (strained yogurt), Avocado Oil, Coconut Oil, Camellia Oil from Japan, Sodium Hydroxide, Lanolin, Agave, Bentonite Clay, Beeswax, Sodium Lactate, Argan Oil, Fragrance & EO's.
Do you have any food allergies: dairy products, nuts, etc? Those with food allergies may also have similar skin contact allergies. Some people are allergic to lanolin. Tertius is fairly heavily scented with both fragrance oils and essential oils. It is possible you could be allergic to one of them.
When trying a new soap, you might want to apply some lather to the inside of your elbow and allow it to remain for several hours. The skin there is similar in sensitivity to your face.