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Obsessive licking is usually a sign of digestive irritation, and the green vomit supports that idea.
Typically, in cases like this, it is reasonable to give a dose of an anti nausea medicine, to see if the problem resolves. If it does not, then a veterinary exam and an x-ray would be recommended in most cases.
Choices for medicine to try include: Pepto-Bismol liquid, 2mL (or a half caplet), OR Pepcid-AC, 1/2 of a 10mg tablet, or Zantac, 1/2 of a 75mg tablet.