You are right to be suspicious. The Lower Muscogee Creeks, calling themselves a tribe, are nothing of the sort. They are a mishmash of individuals who claim Creek ancestry, but most have absolutely no proof. I would be surprised if any have proof of Indian/Creek ancestry.

Keep in mind that the state of Georgia, typical of other southern states such as Alabama and Florida, grant state recognition without asking for any proof that the group or its members constitute an authentic tribe. The group you mentioned is a club, not a tribe.

I suggest you approach your search using standard genealogical practice. First get yourself a good book, either from the library or a bookstore, that gives you the beginner's version of research.

Second, search out each generation starting with yourself, working your way from the known to the unknown, documenting every generation's names, dates and places of birth, death and parents with available documents.

You can come back to this fourm with questions anytime you need to and someone will be here to help you along the way.