I have obsessive-compulsive disorder and major depressive disorder. can i have generalized anxiety disorder too?

YES: Yes- you can also have a generalized aniety disorder- consult with BOTH your psychiateist and psychologist.

Maybe: In Psychiatry there is a riff in between the "lumpers" and the "splitters". As the names imply some will lump together symptoms ( like obsessive compulsive been an anxiety disorder and or anxiety been part of Major Depression) vs. others who would separate if Sx,s are so strong or if they appear at different times. Discuss it w your Doctor. Anyway those 3 disorders could respond to Prozac (fluoxetine).

Yes: All may be coming from the same root cause. Addressing this in therapy, learning where the feelings come from, can be a vital step along the way to learning how to put them into perspective, and in so doing possibly to gain some control over them over time. Meds help, but therapy possibly better in the long-term. Combination of the two is preferable.