if you have dry skin to use special cleansing gel you will feel tight after using it, if you have combination dry +oily skin eg on the t zone maybe you can use it on oily part.
for the moisturiser it may because your skin condition has changes due to external factor because i dont think it adapt well in 5months but change at a sudden. it may due to imbalance hormone or weather etc. anyhow at this moment if you have oil seed, it may a sign of over moisture, if you said its whiteheads, i would say that every skin is naturally grow with white/blackheads which due to oily skin condition
most recommend for professional consultation, above is base my opinion ^