The "injuries" that Tybalt is speaking of in these lines actually refer to events that take place at the Capulet ball in Act I, Scene V. Tybalt feels very insulted to see that Romeo has crashed the ball. Tybalt feels insulted because he assumes Romeo is there to make fun of their party, as we see in Tybalt's lines:
What dares the slave
Come hither, cover'd with an antic face,
To fleer and scorn at our solemnity? (I.v.57-59)
Since he feels that Romeo is there to insult the Capulets, he feels that Romeo's very presence is an insult, or "injury."
Not only that, Tybalt's "injuries" are doubled when Lord Capulet forbids Tybalt to kill Romeo for crashing the ball. Instead, Capulet argues that Romeo bears himself like a true gentleman of his rank and that all of the city knows him to be a "virtuous and well-govern'd youth"; therefore, Capulet insists that Tybalt leave Romeo alone (I.v.71). When Capulet continues to insist, despite Tybalt's proclamation that enduring Romeo's presence would be a shame to the Capulets, Tybalt feels even further insulted by his uncle. Therefore, the "injuries" Tybalt is referring to in Act III, Scene I are the insult Tybalt felt at seeing Romeo at the ball, plus the insult he felt at being disregarded by his uncle.