Yes, contact allergy. Bees wax can cause contact allergy, usually due to a component named propolis or bee glue. Propolis is derived from tree resins and contains known contact allergens (allergy causing substances) such as cinnamic acid, vanillin, components of balsam of peru. Patch tesing by a dermatologist would clarify which allergens are involved and what to avoid in the future.
Yes. Interesting question. Just did a quick search. Beeswax is a complex product containing many proteins. There is propolis, "bee glue", usually mixed in commercial beeswax products, that can cause contact allergy. There r also small amount of pollen usually mixed in beeswax. Whether that amount can cause allergy, it is unsure.