Ex:
My brother asked me if I wanted a pizza or a sandwich.
My brother asked me whether I wanted a pizza or a sandwhich.
Ex:
My brother asked me if I wanted a pizza or a sandwich.
My brother asked me whether I wanted a pizza or a sandwhich.
Both of your sentences talk about the same thing: your brother's query about a choice between pizza or a sandwich.
Both are commonly used.
You may also note that if only one alternative was mentioned, whether will still need a contrast:
My brother asked me if I wanted pizza
My brother asked me whether I wanted pizza or not