Clogged pores/dry skin?

Hi all, I used to have a routine where I would wash my face 2x a day and then moisturize (once in the shower in the morning and once at night). My skin gets really, really dry, so I have to heap mounds of moisturizer onto my face. Recently, my skin has been staying dry and feeling not great even after I put moisturizer on, and also I've noticed that my pores are bumpy and standing out more. Does this mean they're clogged? How can I have dry skin and clogged pores at the same time? Any advice appreciated!