Whether you get your FAA medical certification through the Peterson Aero Club or with another examiner there a number of conditions in which the AME (FAA Aviation Medical Examiner) can issue provided you bring additional documentation. These conditions include: Arthritis, Asthma, Colitis, Glaucoma, Hepatitis C, Hypertension, Migraine & Chronic Headache, Pre-Diabetes, Renal Cancer, Prostrate Cancer, Testicular Cancer.
Prior to making an appointment with any AME go to the following FAA site, download and complete the appropriate worksheet. https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/ame/guide/certification_ws/
The worksheets provide the information CAMI (FAA Civil Aeromedical Institute) requires and allow the AME to issue a medical certificate without, the often, months of back and forth FAA correspondence.
The site for the basic FAA medical application is medxpress.faa.gov