Tybalt's frustration with Romeo in Act III, Scene 1 can actually be explained by something that occurred earlier on in the play. When Tybalt refers to the "injuries that [Romeo] hast done," Tybalt is referring to what occurred at the Capulet's ball.
At the Capulet ball in Act I, Scene 5, Tybalt recognizes Romeo's voice when Tybalt hears him asking a servant who Juliet is. Tybalt is furious to see that Romeo, a Montague, has invaded his family's private ball. Tybalt makes haste to fight with Romeo and to "strike him dead" for the "honour of his kin." However, Tybalt is actually stopped by Lord Capulet. Lord Capulet does not want bloodshed at or near his party, but he also rationalizes that Romeo is reported throughout Verona "to be a virtuous and well-govern'd youth." Therefore, Lord Capulet instructs Tybalt to leave him alone. Tybalt argues with his uncle, but then finally gives in. However, his uncle's treatment infuriates Tybalt even further. Tybalt feels he has been insulted by Romeo in his own house and promises to revenge himself on Romeo soon.
Hence, by the time we get to Act III, Tybalt feels he has been insulted by Romeo for two reasons: 1) Romeo invaded Tybalt's home and family; 2) Tybalt was put down by his uncle. Thus, a frustrated Tybalt also feels that Romeo is responsible his uncle's rebukes, which he feels were insulting.