Cosmetic results from a chemical peel are mostly dependent on depth of peel, chemical agent, and your skin quality. The physical location (physician's office versus a spa or salon) itself should not matter. Patients get better results with deeper peels; however, the recovery time and potential risks are higher. Any location where skin care takes place must be clean & sterile.
Generally speaking fruit peels are very superficial and do not go deep into the skin. Consequently, the results are minimal and treatment must be repeated multiple times to appreciate an effect. Recovery is quick though.
Any treatment which goes deeper into the skin must be performed by a physician. Lastly, skin care starts before and continues after the peel, which your physician can help manage. Certain skin care products are only available from a physician. Best of luck.