I don't have a recommendation for a specific person. However, I d have a recommendation for getting a referral:
1) Contact your local bar association. That can be at the state level, county level, and in some larger metro areas there's even a city bar association. Many will have referral systems that can refer you to a lawyer specializing in SSD/SSI cases.
2) Ask other lawyers who do NOT specialize in SSD/SSI who they have heard of. In my case, I got a referral to my lawyer from my mother-in-law's Estate lawyer. Even if you haven't personally used a lawyer, you may have a friend who has who can get a referral for you. Lawyers network like crazy.
3) Look at National firms: Binder & Binder, Allsup, etc.
I'm not sure what the difference is, lawyer wise, between SSD and SSI cases are, but in a SSD case your payment will be 25% of your first SS check, which will include a certain amount of back payments. The max they can take, without special authorization from SSD is $6,000 OR 25%, whichever is LESS.