Mild burning sensation in rectum and on prostate/anal area after ejaculation and after bowel movement, sometimes after urination. What it could be?

Get tested. You should see a doctor. Conditions to be considered include prostatitis (an infection of the prostate) or proctitis (infection of the anus). Proctitis can occur with a number of sexually transmitted infectious, including gonorrhea, chlamydia, herpes, and syphilis.