I can't say it will go away. I'm pre op, so I can't even speak from experience. But all the research I've done and questions I've asked my doctors lead to the same thing...depression post op is VERY common. Our fat cells store a lot of hormones. So as we burn fat, all those hormones will be released. That's why some people experience a euphoric feeling the first few weeks post op, and the larger majority experiences some depression.
You are doing great by seeking help and managing it with medications. Allow a month to see improvements from the meds. It can be a long wait, but most meds do take at least 4 weeks for any results. If you are seeing no improvement or are feeling worse after a month, try a different medication. Make sure to follow the guidelines for weaning on and off anti depressants and sleep aids though!
Hang in there. It will get better!