Yes, you can be agoraphobic and have an anxiety/panic disorder and qualify for benefits... I have both, and I have been on SS disability since 1999.
The key to getting your claim approved is having LOTS of documentation from doctors stating the exact nature of your problem. (and it certainly didn't hurt that every time I had to talk to an SS representative on the phone I had a panic attack).
How long have you had this?
I had anxious tendencies since I was 4 years old, and when I sent in my application (at age 24) I included my school records and my childhood medical records so that I could show proof that this is a lifelong problem.
You will at some point probably get a letter from them asking you to come to their office for an interview... just so you know- you can insist that you have the interview done by phone. I have never set foot in the SS office- I did everything by phone
You can also go to the SS website to read about the specific medical qualifications that you must meet for your illness. They have (somewhere on the site) a data base of all disabilities (including mental) and the parameters that your illness must fall under to be considered a disability.
If you can print out the SS list and bring it to your doctors office it would be helpful so that you and your doctor will know exactly what SS is looking for in the reports and records that they will request from your doctor.
The entire process of applying for disability can be especially scary for people like us who have anxiety based disorders... but I'll tell you 1 thing that I have learned over the years- It is often easier to prove and get disability for a "mental" disorder than a purely physical one.... you will see the list of my medical conditions in my signature... the anxiety is my only official disability considered by social security.
Best of luck