I get a little bit of that on my chin. I've not heard of having it so deep, but that doesn't mean it isn't common.
Try using an AHA or BHA cream after you shower. These are acids that increase cell turnover to shed your skin faster than it normally comes off. Your pores are clogged and they need clearing - using these might help. You could also try a chemical peel. You can do these at home by yourself; they sell products and kits online for doing it solo, but be careful. You can burn yourself or make things worse. It's at least worth looking into, though.
There's an AHA for sale on this site; you can also use Alpha Hydrox brand, which you can buy at some drugstores or at Ulta. Paula's Choice is a good BHA, but any salicylic acid acne treatment is a BHA - but drugstore brands might not be strong enough. Also lactic acid might help - Amlactin is available at drugstores. But above a certain percentage, it's not PH-balanced, so do a little research on what percentage is best for any of these products.
Don't know if that helps, but hope it does a little.