In Othello, Othello's jealousy takes many forms.  Here are three uses of "jealous" and their implications in the play:

1.  "feeling or showing envy of someone or their achievements and advantages"

Even though he outranks Cassio and Iago and has a more beautiful wife, Othello shows signs of envy.  As a black man in a white world, as a former Muslim in a Christian world, and as an older military man in a young civilian world, Othello suffers from an inferiority complex based on social mores and racial codes.

2.  "feeling or showing suspicion of someone's unfaithfulness in a relationship"

Since his is an "honor culture" that supports the male and devalues the female, Othello sets his relationship up to fail by giving her the handkerchief, expecting her to lock it under key (by being submissive and quiet).

3. "fiercely protective or vigilant of one's rights or possessions"

Othello wants exclusivity with Desdemona: if he can't have her quiet, dutiful, and virginal, then no one will.  His strangling her is an honor killing--the way a vengeful father or brother kills an unfaithful woman so as not to soil the family name.  In the end, Othello equates Desdemona as a status symbol: they rise and fall together.

I would have to say that he absolutely did.  If morbid jealousy is jealousy that takes the form of a disease, Othello caught it and caught it something fierce.  Iago plays him like a fiddle, but the absolute depths of jealousy that he awakes in Othello are really spectacular.

You can also look at the way that the jealousy is connected to Othello's epileptic fits and connect the two to talk about how the jealousy takes on the form and even some symptoms of a disease.

You could also just compare Othello's attitude towards Desdemona and Cassio at the beginning of the play and then at the end (or at the climax) and clearly demonstrate that Othello's jealousy has ravaged his soul just as a disease might have ravaged his body.