Cat Health Questions? Ask a Cat Vet for Answers ASAP.
While the petroleum component of Bag Balm is not harmful, the 8-Hydroxyquinoline component should not be ingested. A few licks would probably not hurt, but you would not want Callie licking it on a chronic basis.
Since your vet has already seen her for this problem, I would consult with them as far as other treatment alternatives if what you have tried is not working. It sounds like you are dealing with allergy problems, so perhaps they can prescribe a trial of antihistamines or even a round of steroids orally to break the itch cycle. Omega 3 fish oils may also be useful.
Good luck with her and please let me know if you have any other questions.