By the time I see a patient with a groin pain they have usually been given a course of NSAIDs already. I hate NSAIDs because of their side effects. Early in my career I lost an old man with a perforated DU which followed Indomethacin (Indocid) given for some trivial pain.
LA (local anaesthetic has two uses, in my opinion. One, if it abolishes the pain at the time, it supports the diagnosis of a mild muscle or ligament tear, except for placebo cases. Especially useful is testing tenderness with muscles tensed and relaxed, to distinguish abdominal wall problems from deeper tenderness. You see this at the neurovascular hilum near McBurney's point. Also, testing resisted movement for pain, such as trunk rotation or extension, which disappears after the LA.
Secondly, it may be curative. What I tell patients, and partly believe, is that minor scarring presses on pain endings, and the injection disrupts and disperses the scarring, giving long-term relief. I have no proof of this from histology of recently injected tissue stained for nerve endings and collagen.
I do this occasionally, perhaps half a dozen times a year, for RIF pain, painful scars, subcostal and xyphoid pain. I am usually delighted with the result. Most patients with a painful xyphoid (actually the tendinous attachment) are referred with epigastric pain and have had a heap of tests including ECGs, endoscopy, and trails of antidepressants.
Surgeons have an advantage in carrying out injection therapy because you can tell which layers you are going through.