It is unclear to me what is going on here. In particular, I am uncertain of the association between what you are describing as skin symptom and then also throat symptoms.
The throat symptoms may be associated with a number of things, including asthma, nasal allergies (allergic rhinitis) and sinus problems
. These conditions are often made worse in humid conditions because the allergens (mold and mites) that are associated with the allergic component of these conditions proliferate in humid climates. Also, some variants of asthma are worsened by cold air, which triggers constriction of the air passages.
Chronic skin rash may be part of a spectrum of allergy (atopy). Many people with sinus, asthma, or nasal allergy symptoms also have skin allergies or eczema
. At its most basic level, these rashes are treated by keeping the skin well protected and well moisturized with a thick skin care product ("greasy" products are better at protecting the skin than lotions). Additionally, particularly troublesome patches of redness or itchiness can be treated with an over the counter steroid cream.
I strongly recommend talking to your primary care doctor
to help you tie all these symptoms together and arrive at a confirmed diagnosis and plan for treatment!