テニスでひじを痛めました。

tennis

indicates location of action; at; in; indicates time of action; indicates means of action; cause of effect; by; and then; so; indicates continuing action; indicates certainty, emphasis, etc.

elbow

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to hurt; to injure; to cause pain; to harm; to damage; to spoil; to worry; to bother; to be grieved over; to afflict; to cause financial loss; to hurt one's pocket