How do you deal with family who doesn’t believe you on your sobriety

Obviously it’s my fault, but now I’m in constant fear, shame and anxiety that no matter what i do or act i will always be labeled an alcoholic which is fair and i acknowledge it but it’s a constant battle now, if i get sick with the flu like a normal person everyone thinks I’m drinking or in a hole again, how can i convince people that I’m really trying to go on in life