Yes, make an appointment with a veterinary dermatologist and get the dog diagnosed.
Pruritus is not a typical response to anxiety. Your vet is correct.
She probably has atopic dermatitis/environmental allergies. There is no cure, allergies wax and wane. There is effective treatment but it will cost a few bucks.
Environmental allergies tend to show up between ages 1 to 3 and get worse with age.
Maybe that was why she was given up/abandoned.
Don’t keep changing the food and trying all kinds of bogus remedies, it won’t work.
Please see my posts, you may find something helpful.
/forums/search/atopic+dermatitis/
Take the dog out for bathroom breaks every 2 hours and first thing in the morning and the last thing before bedtime. Try to be patient, it sounds like this dog has been through a lot.
When her skin condition is properly diagnosed and treated you may notice a much more relaxed and comfortable dog.
Regarding the separation anxiety you may want to talk to your vet about medication, as the dog continues to stabilize after a few months to a year she can be tapered off. It doesn’t have to be forever.
