It depends. There are various factors which might contribute to bags under the eyes, and you really need a doc to see and examine this, and do a full check-up of your general health, and consider what may be going on.
By the way, are you meaning real pouches of baggy skin under the eyes, or perhaps dark semi-circles in the skin under the eyes ?
A doc would want to consider why you're sleeping badly, and what best to do about that. You don't mention whether you are taking any treatment for your depression, as some antidepressants may cause insomnia, while others can usefully relieve it.
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