According to the ACAAI:
Where Should Allergy Shots Be Given? This type of treatment should be supervised by a specialized physician in a facility equipped with proper staff and equipment to identify and treat adverse reactions to allergy injections. Ideally, immunotherapy should be given in your allergist / immunologist’s office. If this is not possible, your allergist / immunologist should provide the supervising physician with comprehensive instructions about your allergy shot treatments.
Are There Risks? Serious reactions to allergy shots are rare. When they do occur, they require immediate medical attention. Symptoms of an anaphylactic reaction can include swelling in the throat, wheezing or tightness in the chest, nausea and dizziness. Most serious reactions develop within 30 minutes of the allergy injections. This is why it is recommended you wait in your doctor’s office for at least 30 minutes after you receive allergy shots.