Sensitive Skin and Fragrance

If your skin reacts unpredictably to products with nothing obvious in common, fragrance is the first thing to rule out.
Unscented is not fragrance-free
"Unscented" often means a masking fragrance was added to cover the smell of the base. "Fragrance-free" is the term that means what you want it to mean.
Irritation versus allergy
Irritation appears quickly, on first exposure, and settles when you stop. Allergic contact dermatitis can take days to develop and worsens with each repeat exposure. The second kind will not resolve by pushing through.

Finding the culprit
Strip back to a plain cleanser, a fragrance-free moisturiser, and sunscreen for two weeks. Then reintroduce one product a week. It is slow and it is the only method that actually identifies the cause.
When to get help
Reactions that recur, spread, or do not settle deserve a professional opinion. Formal patch testing can identify the specific allergen instead of leaving you guessing.