I wouldn't use tea tree where there is any broken skin. It can be very harsh and I have heard (on this forum) it can be poisonous to dogs. Aloe vera gel is very soothing and calming for itchy skin, and can also be taken internally so should be harmless if licked. You can either get it in a tube (very good for human use too, for minor burns, sunburn, rashes, insect bites or just as a moisturiser) - or you can get a plant. Cut off a leaf, split it open and rub the inside of the leaf over the skin.
There's also a company Denes that make herbal products for dogs and cats. There make a mite cream and a hot itch lotion, both of which contain herbs that help inflamed itchy skin. You can get it in some health food shops and some pet shops too.