You're right to pick up on the reference "My Lord" as an indication that Othello has some kind of important position, but it can be a little bit tricky to figure out what that role is. Let's take a look at the conversation between Iago and Roderigo in the first scene of the play. Sometimes you can find important details that you might have missed at first because you didn't know the characters yet.
Was Othello a king? A prince? He's referred to as My Lord" but I'm not sure of his actual title."
Within moments of the opening scene, we hear Iago complaining to Roderigo about being passed up for a promotion to become a lieutenant. "Three great ones of the city, / In personal suit to make me his lieutenant . . . / But he . . . evades them with a bombast circumstance. / . . . says he, 'I already chose my officer.'" It seems that Iago is a soldier with a grudge against his superior. Iago feels jilted for getting a lesser post: "He [Cassio], in good time, must his lieutenant be, / And I — God bless the mark! — his Moorship's ancient."
I'm sure you're familiar enough with the play by now to recognize that "his Moorship" refers to Othello. So, from this exchange, you can safely assume that Othello is a high ranking officer of the Venetian army.
In the second scene, Iago and Othello are talking and are then joined by Cassio, who says to Othello, "The Duke does greet you general; / And he requires your haste-post-haste appearance." So, it seems that Othello is, in fact, an army general. As you continue reading Act I, you'll find even more instances when the other characters address Othello as general.