Is alcohol in skincare always bad?

No. Fatty alcohols, such as cetyl and stearyl alcohol, have different roles from ethanol and can help a moisturizer feel soft and creamy. Different alcohols serve very different functions, so I would look at the exact ingredient and full formula instead of rejecting the category.

The word “alcohol” does not tell you enough

The word alcohol alone is not enough to reject a product. Judge the whole formula and your response. Repeated burning or dryness is a reason to reconsider the product, whatever its label says.