I know just how you feel, I have a little terrier and a largr rat terrier, they both do the licking and scratching thing, for years I use to get an alergy shot for them, it helped for several months, tried topical lotions and creams, always comes back, I am now of the opinion it is a mite that burrows into the skin, I have found a dip type solution at the local feed store, and I try to dip them several times a year, this has helped, but the winter weather is a bad time for dry skin, that is a factor too. over the years I have made shirts for them, the little dog likes her clothes, the rat terrier does not. I have been using chldren tee shirts and sweats and modifing them to fit with a lab I guess a women's small size may work, measure the back of the lab, from the neck to near the tail, measure the girth, if you have an old sweatshirt cut a seam on the front, don't go any higher then the arm hole
this way you can slip the head in and try to get the legs in the sleeves, then pull the sweat over the back, on the under side check how much fabric needs to be removed to make a closer fit. I trim and sew a binding on that leaving enough room for snaps or button and buttonholes. this way I can close up the shirt. Has been working rather well, but this year I found a pattern in kwik sew # 3076 that has a wonderful 4 legged shirt you can make out of fleece and any stretchy fabric, hope you can get something going from this Rene

Here is a link that might be useful: Sewthankful pet patterns