I agree with Sendro, but will add that you only need to use the "yo" if the context makes it ambiguous about who the subject of the verb is. That is, if it could be él or ella (it can't be usted in your example), then you might need to use the pronoun. For example, the speaker could be talking about Juan, in which case the translation would be "When you told me that he had passed the test, I couldn't believe it." If your context makes such a situation possible, then you need to include the pronoun.
The second "yo," however, is unnecessary because the "me" makes it clear who the subject is.