Mould allergy aggarvated by AC units is a good possibility but hotel rooms are notorious to harbour dust mites and dust allergy
would be likely.
Skin tests to moulds, dusts, cockroach need to be done to exclude these allergies. If you are using any eye maskara or facial cleaning products, you need to get a patch test
in order to exclude a delayed chemical hypersensitivity
Skin prick tests and patch tests are different, so you need to see an Allergist or a Dermatologist
to sort this out.