Maybe the propylene glycol, like Kathymack said. It rarely causes irritant contact dermatitis, but it's in so much stuff, including food, you would definitely want to consult an allergist to know for sure if it affects you.
BHT is a preservative in Vanicream. BHT is a synthetic antioxidant and preservative often used in cosmetics, foods and industrial compounds for its ability to deter rancidity in oils and improve the shelf-life of water-based products. BHT is a known allergen and skin sensitizer.
Another cream widely recommended by dermatologists is CeraVe
. Here are the ingredients: Water (Purified), Glycerin, Ceteareth 20, Capric/Caprylic Stearic Triglyceride, Behentrimonium Methylsulfate/Cetearyl Alcohol, Cetearyl Alcohol, Ceramide 3, Ceramide 6 11, Ceramide 1, Hyaluronic Acid, Cholesterol, Petrolatum, Dimethicone, Potassium Phosphate, Dipotassium Phosphate, Sodium Lauroyl Lactylate, Disodium EDTA, Phenoxyethanol, Methylparaben, Propylparaben, Phytosphingosine, Carbomer, Xanthan Gum