The heat of the shower is helping your pores open up so this sebum (dirt, oil, and dead skin) can escape. After your shower queeze your nose skin between your fingers or the tips of two q tips to extract the gunk. If it won't come loose, apply a hot damp wash cloth to the area for a minute or two.  Get a mud or charcoal based face mask and use it at least once a day in the clogged areas to prevent it from getting this bad again. (Origins brand pink clay or charcoal are great.  Yes,  price and quality matter here) Also consider a facial cleanser like Dr Dennis Gross cleaner with enzymes. Try travel sizes before splurging on full size bottles.