Will all allergy shots cause permanent divots on my arms?

No. On rare occasions patients on immunotherapy develops little hard lumps under the skin. These are probably granulomas. I say probably because we don't biopsy them. They resolve spontaneously in a few months and possibly contribute to a better response to allergy shots. I've never seen a divot from an allergy injection.
No. Allergy injections containing allergens as given by an allergist do not leave "divots". However, injections of steroids can cause fat necrosis and "divots" which are irreversible. Just another good reason not to receive that large dose of steroid like kenalog (triamcinolone).