More likely boredom than anxiety. Maybe you can increase exercise and leave her with more things to do. Various people here have posted on toys they leave for their dogs to alleviate boredom and keep them occupied while they are away at work, a search may give some ideas.
Whatever the reason, I think it is similar to licking lips and rubbing noses as children sometimes do. It feels good when they lick it, but it perpetuates the problem and leads to more licking since it feels better while they do it. My dog does it sometimes as well. I think the toy idea is a good one, but I haven't found any toy that interests my dog, even when I am home. She does love Greenies and Bully sticks, but she always saves them until I get home for some reason, then she runs over, gives one to each of us, and cuddles up to enjoy hers.
The trick to healing skin soreness and hot spots is to break the cycle of chewing/licking, but that isn't easy of course. I tried a bitter apple spray with limited success. Benadryl really seems to help Sully when it is really bad. The vet can help with dosage. We also tried prednisone. WAY to many side-effects in my mind. The best thing so far is something I read about on this site somewhere called Nu-Stock. I had to order it online. It was only about $12. for a large tube. The smell alone should deter licking, but it will get on everything she walks on and the smell permeates the house. II have to wash her bedding twice after she wears it for a day.Sully got some on my leather sofa and I was able to wash it out with mild soap and water, but it is easier to use it when you are home or the dog is somewhat contained. It does seem to help but it is unpleasant and requires extra bathing and laundering. It recommends using it every three days on the tube, but it does say it is safe for dogs, even for cats. May be worth trying. Sully allows me to rub her feet but not happily. She does allow me to put aloe vera and Nu-Stock on them though, I think because it feels good. I hope you don't have to resort to muzzling her or risking a bite. Hope you find something soon that helps Milly!
I always leave the television on when I am out too. Not sure if it helps. I thought it was weird that Sully won't eat anything when I am out, but I guess she isn't alone in that quirk. I had a couple of events that kept me away for much of the weekend so I got a "sitter." She did eat then, but she knows the woman well. She can easily wait for up to 12 hours to go to the bathroom, but I try not to leave her more than 5-6 hours due to her separation anxiety. She doesn't cry, bark, or destroy things, thank God, but she tries to sneak out whenever I leave and she makes crazy happy noises and refuses to leave my side for at least an hour after I get home. If I get on the floor to greet her she climbs on my lap and it is hard to move her. It feels like she's magnetized or Velcroed to my lap.
Griffin licks his paws until they're red because of seasonal allergies. He's only allergic from August thru November; after the first frost he's fine. Maybe ask the vet about giving her some Benadryal.