Mississippi Subscriber
Answer: In this instance, you are correct that you should use 95115 (Professional services for allergen immunotherapy not including provision of allergenic extracts; single injection).
The difference between the codes is that 95120 (Professional services for allergen immunotherapy in prescribing physician's office or institution, including provision of allergenic extract; single injection) includes the allergenic extract provision, but 95115 doesn't. Code 95115 instead describes injection administration without serum provision. Both codes include professional services, such as monitoring the patient for an adverse reaction, necessary for allergen immunotherapy.
Since your example describes a patient who brings in his serum, you would use 95115 in this instance. If your family physician provided the serum, you would instead report 95120.