this is often seen. need to discuss the skin products you have been using, and the lifestyle eg sports you engaged in.
you seem to have two problems. Firstly use appropriate moisturizer for dry sensitive skin like physiogel and anti-inflammatory cream. as for your blackheads, it should be extracted carefully by therapist and given some topical antibiotics. After the dry and sensitive skin condition has improved, can consider a salicylate peel with more moisturizer for sensitive skin.
thanks