From your description, it does seem like you have both sensitive skin with prominent blackheads or comedones.
To get rid of blackheads, there are creams like tretinoin and salicylic acid creams that can be precribed. Extraction of blackheads can also be considered. Many of the prescribe creams like tretinoin cream and salicylic acid though can be potentially irritating and may aggravate dry and sensitive skin.
You may consider visiting a dermatologist who can assess your skin sensitivity and precribe the most appropriate treatment for you.
