Is it normal to be diagnosed w/an autoimmune disease after beating cancer?

No: Unless, you have had a bone marrow transplant. Many people after a bone marrow transplant experience graft-versus-host disease, in which the patient's new bone marrow attacks other normal body tissues.

It is not normal: Do not believe these are related events. However one can envision that if one had had chemotherapy, the chemotherapy may have affected the body's ability to regulate immune function leading to autoimmune disease- this is only a guess and I have no proof for this.

Yes it can: I have seen sjogren's and rheumatoid diagnosed after lymphoma. Have seen rheumatoid arthritis and psoriatic arthritis diagnosed after breast and prostate. Are they a coincidence---hard to say, but in the case of lymphoma---rituxan is used to treat lymphoma and it also approved to treat rheumatoid as well---it targets the same cd19/cd20 cell that is involved in both processes.