Hi Whitney good for you for taking back the puppy
You can use a people conditioner, work it deep into the matted hair and some of the matting will come out by separting the hairs with your fingers as it penitrates. Remember the Yorkies hair is very much like our own so if you can get a mat out of yours you can get them out of theirs in most cases.
As to the dry skin it could just be the dandruff buildup if there is no visual abnormal skin markings the conditioning should help the skin as well as a healthy diet...
Since you have access to the computer instead of driving into town for your products order them online some pet stores offer free delivery with a minimum.
A quality puppy food should also help his skin if you want to suppliment pet-tabs or Nu-vet vitamins are very good.
hope this helps and your puppy is lucky to have you back!