Is surgery the only option to fix snapping triceps syndrome?

Yes. Typically surgery is used to correct the mechanical symptoms associated with snapping triceps syndrome. However, conservative treatment is an option if the patient is willing to accept the continuation of symptoms. There is no negative consequence to conservative treatment.
No. Avoid all aggravating exercises e.g. Push-ups, weight lifting & repetitive elbow flexion. Nsaids, splinting, rehab, and steroid injections can all help. If the symptoms persist after 3 to 6 months, surgery should be considered.