I never got the Depo shot, and that is precisely why - I was already being treated for depression (on antidepressants) and I had heard that the Depo shot can worsen depression.
I'm not sure what dosage of Paxil you are on, or how long you have been on it, but I would NOT recommend stopping the medication suddenly - that can make you feel even worse, PLUS throw in a load of physical symptoms such as headaches, nausea, dizziness, a shock-like feeling, etc. If you are going to stop the medicine, I would highly recommend consulting with a doctor.
I don't remember as clearly the specifics about the withdrawal symptoms I experienced if I missed my Paxil since it was so long ago, but I think I experienced this weird kind of shock-like symptom, usually mostly in the head/face, especially when I move my eyes, with all of the antidepressants I have been on. From what I've read, Paxil seems to be one of the worst when it comes to withdrawal symptoms. (Effexor is even -worse- in my experience - I'd think twice before trying that one). Here's one site you can check out about some information on Paxil withdrawal: http://www.quitpaxil.info/Main/symptoms.htm
I would talk to a doctor as soon as possible, and if it were me, I would consider an alternative birth control method since Depo can worsen depression (and even cause it from what I gather from some of the other responses).
Best of luck!