Generally I avoid treating the lower eyelid area with BOTOX. This area is best addressed with fillers. When BOTOX is done well around the brow, we now understand from functional MRI studies that it truly makes us feel psychologically happier beyond the boost we get when we feel we look better. Specifically muscles at the brow are responsible for facial expressions associated with anger. When these are blocked the normal feel back that send that little message "mad" to the hippocampus is gone, you feel better.
What is less well appreciated but I have seen it several times, is that when muscles that make the smile are blocked by BOTOX, the result is very dysphoric and unpleasant. The effect must be central in the brain because the weakness in the face is generally pretty subtle. Yet I have seen people who become so depressed by the dysphoric feeling that they are essentially disabled until the medication wears off.
When will this happen. The cases I have seen took about 4 months. However, I will caution you that it might last as long as 6 months but unlikely longer than that. At this point there may be little value in being treated with antidepressants if you are clinically depressed. Still there may be a role for seeing a psychotherapist once a week so you have a place to talk about how hard the process has been and what it has meant for you.